Wynik

Rozwiazanie

Wykorzystane biblioteki

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tidyr)
library(knitr)
library(DescTools)
library(readxl)
library(caret)
## Loading required package: lattice
## Loading required package: ggplot2
## 
## Attaching package: 'caret'
## The following objects are masked from 'package:DescTools':
## 
##     MAE, RMSE
library(plotly)
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
library(kableExtra)
## 
## Attaching package: 'kableExtra'
## The following object is masked from 'package:dplyr':
## 
##     group_rows

Wczytywanie dannych, zmianna nazw kolumn

Z pakietu ‘readxl’ wykorzystano funkcję ‘read_excel’. Jak się okazuje, wiersze dla kolumny ‘PATIENT_ID’ są złączone ze sobą w excelu, natomiast po wczytaniu tylko jeden wiersz dla danego id nie otrzymuje wartość NaN.

orig_data_csv <- read_excel("wuhan_blood_sample_data_Jan_Feb_2020.xlsx")

kable(head(orig_data_csv, 5)) %>%
  kable_styling(bootstrap_options = "basic",
                full_width = F) %>%
    scroll_box(width = "100%", height = "100%")
## Warning in do.call(data.frame, c(x, alis)): unable to translate 'Tumor necrosis
## factor<U+03B1>' to native encoding
## Warning in do.call(data.frame, c(x, alis)): unable to translate '<U+03B3>-
## glutamyl transpeptidase' to native encoding
PATIENT_ID RE_DATE age gender Admission time Discharge time outcome Hypersensitive cardiac troponinI hemoglobin Serum chloride Prothrombin time procalcitonin eosinophils(%) Interleukin 2 receptor Alkaline phosphatase albumin basophil(%) Interleukin 10 Total bilirubin Platelet count monocytes(%) antithrombin Interleukin 8 indirect bilirubin Red blood cell distribution width neutrophils(%) total protein Quantification of Treponema pallidum antibodies Prothrombin activity HBsAg mean corpuscular volume hematocrit White blood cell count Tumor necrosis factorα mean corpuscular hemoglobin concentration fibrinogen Interleukin 1β Urea lymphocyte count PH value Red blood cell count Eosinophil count Corrected calcium Serum potassium glucose neutrophils count Direct bilirubin Mean platelet volume ferritin RBC distribution width SD Thrombin time (%)lymphocyte HCV antibody quantification D-D dimer Total cholesterol aspartate aminotransferase Uric acid HCO3- calcium Amino-terminal brain natriuretic peptide precursor(NT-proBNP) Lactate dehydrogenase platelet large cell ratio Interleukin 6 Fibrin degradation products monocytes count PLT distribution width globulin γ-glutamyl transpeptidase International standard ratio basophil count(#) 2019-nCoV nucleic acid detection mean corpuscular hemoglobin Activation of partial thromboplastin time High sensitivity C-reactive protein HIV antibody quantification serum sodium thrombocytocrit ESR glutamic-pyruvic transaminase eGFR creatinine
1 2020-01-31 01:09:00 73 1 2020-01-30 22:12:47 2020-02-17 12:40:09 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 7.415 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
NA 2020-01-31 01:25:00 73 1 2020-01-30 22:12:47 2020-02-17 12:40:09 0 NA 136 NA NA NA 0.6 NA NA NA 0.3 NA NA 105 10.7 NA NA NA 11.9 65.8 NA NA NA NA 91.8 39.2 3.54 NA 347 NA NA NA 0.8 NA 4.27 0.02 NA NA NA 2.33 NA 11.9 NA 40.8 NA 22.6 NA NA NA NA NA NA NA NA NA 39.9 NA NA 0.38 16.3 NA NA NA 0.01 NA 31.9 NA NA NA NA 0.12 NA NA NA NA
NA 2020-01-31 01:44:00 73 1 2020-01-30 22:12:47 2020-02-17 12:40:09 0 NA NA 103.1 NA NA NA NA 46 33.3 NA NA 8.3 NA NA NA NA 4.3 NA NA 69.3 NA NA NA NA NA NA NA NA NA NA 8.5 NA NA NA NA 2.29 4.33 NA NA 4 NA NA NA NA NA NA NA 3.9 33 418 21.2 2.02 NA 306 NA NA NA NA NA 36 24 NA NA NA NA NA 43.1 NA 137.7 NA NA 16 46.6 130
NA 2020-01-31 01:45:00 73 1 2020-01-30 22:12:47 2020-02-17 12:40:09 0 NA NA NA 13.9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 91 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 2.2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA 1.06 NA NA NA NA NA NA NA NA NA NA NA NA
NA 2020-01-31 01:56:00 73 1 2020-01-30 22:12:47 2020-02-17 12:40:09 0 19.9 NA NA NA 0.09 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 7.35 NA NA NA NA NA NA NA NA NA NA NA NA NA NA 60 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

Ponieważ mogą wystąpić pewne problemy z kodowaniem, wykorzystano funkcj ‘make.names’, aby zapewnić poprawne nazwy atrybutów

orig_data_df <- dplyr::as_tibble(orig_data_csv) %>% 
                rename_with(~make.names(.x, unique = T), unique = TRUE)

Uzupełnienie identyfikatora

Ponieważ w poprzedniej podsekcji stwierdzono brakujące identyfikatory w wierszach przynależących do konkretnego pacjenta, uzupełniono je za pomocą funkcji ‘fill’ pakietu ‘tidyr’.

new_data_df <- orig_data_df %>% fill(PATIENT_ID) %>% filter(!is.na(RE_DATE))
group_by_id <- new_data_df %>% group_by(PATIENT_ID)

Analiza danych

Analiza wieku pacjentów

Poniższy wykres przedstawia rozkład wieku pacjentów.

age_vector <- group_by_id %>% distinct(age) %>% ungroup()

hist_age <- ggplot(data=age_vector, aes(x=age)) + 
            geom_histogram(binwidth=1, stat = 'bin', fill='steelblue', color='black') + 
            labs(x='Age', y='Count', title='Age histogram') + 
            scale_x_continuous(n.breaks = 20) +
            scale_y_continuous(n.breaks = 10) + 
            theme_classic()
      
ggplotly(hist_age)

Zakres wieku jest duży - od 18 do 95 lat. Dlatego można podzielić ten rozkład na 3 grupy - ludzi młodych(Young), w wieku średnim(Mid) oraz starych (Old).

hist_age_grouped <- ggplot(data=age_vector, aes(x=age)) + 
            geom_histogram(breaks=c(age_min, mid_start, old_start, age_max), stat = 'bin', fill='steelblue', color='black') + 
            labs(x='Age', y='Count', title='Age histogram by groups.', position='dodge2') + 
            scale_y_continuous(n.breaks = 10) +
            scale_x_continuous(breaks=c(age_min, mid_start, old_start, age_max)) + 
            theme_classic() + 
            annotate(geom='text', x=(mid_start+age_min)/2, y=10, label='Young') + 
            annotate(geom='text', x=(old_start+mid_start)/2, y=10, label='Mid') + 
            annotate(geom='text', x=(age_max+old_start)/2, y=10, label='Old')
ggplotly(hist_age_grouped)

Zauważalne jest, że liczba osób młodych do reszty jest mała. Można przypuszczać, że osoby młode albo są bardziej odporne albo ich stan zdrowotny nie pogorszył się w takim stopniu, aby musieli zostać umieszczeni w szpitalu.

Stosunek liczby ludzi młodych do wszystkich pacjentów: 18.01%
Stosunek liczby ludzi w średnim wieku do wszystkich pacjentów: 41.27%
Stosunek liczby ludzi starych do wszystkich pacjentów: 40.72%

Analiza płci pacjentów

gender_vector <- group_by_id %>% distinct(gender) %>% ungroup()

hist_gender <- ggplot(data=gender_vector, aes(x=gender)) + 
            geom_histogram(binwidth=1, stat = 'bin', fill='steelblue', color='black') + 
            labs(x='Gender', y='Count', title='Gender histogram') + 
            scale_x_continuous(breaks = c(1, 2), label=c('Male', 'Female')) + 
            theme_classic()
      
ggplotly(hist_gender)

Stosunek liczby mężczyzn do wszystkich pacjentów: 58.73%
Stosunek liczby kobiet do wszystkich pacjentów: 41.27%

Analiza stanu (outcome) pacjentów.

outcome_vector <- group_by_id %>% distinct(outcome) %>% ungroup()

hist_outcome <- ggplot(data=outcome_vector, aes(x=outcome)) + 
            geom_histogram(binwidth=1, stat = 'bin', fill='steelblue', color='black') + 
            labs(x='Outcome', y='Count', title='Outcome histogram') + 
            scale_x_continuous(breaks = c(0, 1), label=c('Survived ', 'Died')) + 
            theme_classic()

ggplotly(hist_outcome)

Stosunek pacjentów, którzy przeżyli do wszystkich pacjentów: 54.02%
Stosunek pacjentów, którzy nie przeżyli do wszystkich pacjentów: 45.98%

Analiza próbek krwii

Wypełnienie wartości pustych

Wartości przed wypełnieniem

Z poniższej tabeli można zauważyć problem z dużą liczbą komórek o wartości NaN.

before_fill <- new_data_df[, c(1, 8:ncol(new_data_df))]

kable(summary(before_fill[, 8:ncol(before_fill)])) %>%
  kable_styling(bootstrap_options = "basic",
                full_width = F) %>%
    scroll_box(width = "100%", height = "100%")
Interleukin.2.receptor Alkaline.phosphatase albumin basophil… Interleukin.10 Total.bilirubin Platelet.count monocytes… antithrombin Interleukin.8 indirect.bilirubin Red.blood.cell.distribution.width neutrophils… total.protein Quantification.of.Treponema.pallidum.antibodies Prothrombin.activity HBsAg mean.corpuscular.volume hematocrit White.blood.cell.count Tumor.necrosis.factor.U.03B1. mean.corpuscular.hemoglobin.concentration fibrinogen Interleukin.1ß Urea lymphocyte.count PH.value Red.blood.cell.count Eosinophil.count Corrected.calcium Serum.potassium glucose neutrophils.count Direct.bilirubin Mean.platelet.volume ferritin RBC.distribution.width.SD Thrombin.time X…lymphocyte HCV.antibody.quantification D.D.dimer Total.cholesterol aspartate.aminotransferase Uric.acid HCO3. calcium Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. Lactate.dehydrogenase platelet.large.cell.ratio Interleukin.6 Fibrin.degradation.products monocytes.count PLT.distribution.width globulin X.U.03B3..glutamyl.transpeptidase International.standard.ratio basophil.count… X2019.nCoV.nucleic.acid.detection mean.corpuscular.hemoglobin Activation.of.partial.thromboplastin.time High.sensitivity.C.reactive.protein HIV.antibody.quantification serum.sodium thrombocytocrit ESR glutamic.pyruvic.transaminase eGFR creatinine
Min. : 61.0 Min. : 17.00 Min. :13.60 Min. :0.00 Min. : 5.00 Min. : 2.50 Min. : -1.0 Min. : 0.300 Min. : 20.00 Min. : 5.000 Min. : 0.100 Min. :10.60 Min. : 1.7 Min. :31.80 Min. : 0.020 Min. : 6.00 Min. : 0.000 Min. : 61.60 Min. :14.50 Min. : 0.13 Min. : 4.00 Min. :286.0 Min. : 0.500 Min. : 5.00 Min. : 0.800 Min. : 0.000 Min. :5.000 Min. : 0.100 Min. :0.000 Min. :1.650 Min. : 2.760 Min. : 1.000 Min. : 0.06 Min. : 1.600 Min. : 8.50 Min. : 17.8 Min. : 31.30 Min. : 13.00 Min. : 0.000 Min. :0.020 Min. : 0.210 Min. :0.100 Min. : 6.00 Min. : 43.0 Min. : 6.30 Min. :1.170 Min. : 5 Min. : 110.0 Min. :11.20 Min. : 1.500 Min. : 4.00 Min. : 0.010 Min. : 8.00 Min. :10.10 Min. : 3.00 Min. : 0.840 Min. :0.000 Min. :-1 Min. :20.4 Min. : 21.80 Min. : 0.10 Min. :0.05 Min. :115.4 Min. :0.010 Min. : 1.00 Min. : 5.00 Min. : 2.00 Min. : 11.00
1st Qu.: 459.5 1st Qu.: 54.00 1st Qu.:27.40 1st Qu.:0.10 1st Qu.: 5.00 1st Qu.: 7.40 1st Qu.:109.0 1st Qu.: 2.800 1st Qu.: 74.00 1st Qu.: 8.675 1st Qu.: 3.800 1st Qu.:12.00 1st Qu.:65.1 1st Qu.:61.00 1st Qu.: 0.040 1st Qu.: 65.00 1st Qu.: 0.000 1st Qu.: 86.90 1st Qu.:33.50 1st Qu.: 4.94 1st Qu.: 6.70 1st Qu.:333.0 1st Qu.: 3.050 1st Qu.: 5.00 1st Qu.: 4.000 1st Qu.: 0.460 1st Qu.:6.000 1st Qu.: 3.680 1st Qu.:0.000 1st Qu.:2.270 1st Qu.: 3.950 1st Qu.: 5.550 1st Qu.: 3.09 1st Qu.: 3.225 1st Qu.:10.10 1st Qu.: 377.2 1st Qu.: 38.50 1st Qu.: 15.60 1st Qu.: 3.925 1st Qu.:0.040 1st Qu.: 0.603 1st Qu.:3.010 1st Qu.: 19.50 1st Qu.: 183.2 1st Qu.:21.00 1st Qu.:1.980 1st Qu.: 150 1st Qu.: 218.0 1st Qu.:25.60 1st Qu.: 4.772 1st Qu.: 4.00 1st Qu.: 0.270 1st Qu.:11.10 1st Qu.:29.70 1st Qu.: 22.00 1st Qu.: 1.030 1st Qu.:0.010 1st Qu.:-1 1st Qu.:29.7 1st Qu.: 35.30 1st Qu.: 5.70 1st Qu.:0.07 1st Qu.:137.7 1st Qu.:0.150 1st Qu.: 14.00 1st Qu.: 16.00 1st Qu.: 63.58 1st Qu.: 58.00
Median : 676.5 Median : 69.50 Median :32.20 Median :0.20 Median : 5.90 Median : 10.70 Median :178.0 Median : 5.700 Median : 86.00 Median : 16.000 Median : 5.400 Median :12.60 Median :82.4 Median :65.90 Median : 0.050 Median : 81.00 Median : 0.010 Median : 90.10 Median :36.60 Median : 7.72 Median : 8.60 Median :343.0 Median : 4.120 Median : 5.00 Median : 5.985 Median : 0.800 Median :6.500 Median : 4.140 Median :0.010 Median :2.360 Median : 4.410 Median : 6.990 Median : 5.85 Median : 4.800 Median :10.80 Median : 711.0 Median : 40.90 Median : 16.80 Median :11.450 Median :0.060 Median : 2.155 Median :3.630 Median : 27.00 Median : 243.7 Median :23.50 Median :2.080 Median : 585 Median : 340.0 Median :30.90 Median : 19.265 Median : 17.90 Median : 0.410 Median :12.40 Median :32.70 Median : 34.00 Median : 1.140 Median :0.010 Median :-1 Median :30.9 Median : 39.20 Median : 51.50 Median :0.09 Median :140.4 Median :0.210 Median : 28.00 Median : 24.00 Median : 87.90 Median : 76.00
Mean : 907.2 Mean : 82.47 Mean :32.01 Mean :0.21 Mean : 16.07 Mean : 16.70 Mean :184.3 Mean : 6.155 Mean : 85.32 Mean : 83.088 Mean : 6.889 Mean :13.07 Mean :77.6 Mean :65.30 Mean : 0.132 Mean : 78.55 Mean : 8.306 Mean : 90.39 Mean :36.55 Mean : 15.60 Mean : 11.58 Mean :342.8 Mean : 4.294 Mean : 6.51 Mean : 9.589 Mean : 1.017 Mean :6.484 Mean : 9.288 Mean :0.039 Mean :2.355 Mean : 4.509 Mean : 8.889 Mean : 7.81 Mean : 9.887 Mean :10.91 Mean : 1379.1 Mean : 42.44 Mean : 18.17 Mean :15.392 Mean :0.117 Mean : 7.943 Mean :3.689 Mean : 46.53 Mean : 276.1 Mean :23.14 Mean :2.078 Mean : 3669 Mean : 474.2 Mean :31.77 Mean : 112.308 Mean : 61.35 Mean : 0.526 Mean :13.01 Mean :33.24 Mean : 55.34 Mean : 1.313 Mean :0.017 Mean :-1 Mean :31.0 Mean : 41.52 Mean : 76.24 Mean :0.10 Mean :141.6 Mean :0.212 Mean : 33.69 Mean : 38.86 Mean : 81.56 Mean : 109.93
3rd Qu.:1155.5 3rd Qu.: 95.00 3rd Qu.:36.60 3rd Qu.:0.30 3rd Qu.: 12.35 3rd Qu.: 16.77 3rd Qu.:248.0 3rd Qu.: 8.600 3rd Qu.: 97.00 3rd Qu.: 35.200 3rd Qu.: 8.000 3rd Qu.:13.70 3rd Qu.:92.3 3rd Qu.:70.45 3rd Qu.: 0.070 3rd Qu.: 95.00 3rd Qu.: 0.010 3rd Qu.: 93.90 3rd Qu.:39.90 3rd Qu.: 12.72 3rd Qu.: 11.50 3rd Qu.:350.0 3rd Qu.: 5.480 3rd Qu.: 5.00 3rd Qu.:11.400 3rd Qu.: 1.310 3rd Qu.:7.294 3rd Qu.: 4.650 3rd Qu.:0.060 3rd Qu.:2.440 3rd Qu.: 4.870 3rd Qu.:10.260 3rd Qu.:10.95 3rd Qu.: 8.275 3rd Qu.:11.50 3rd Qu.: 1425.2 3rd Qu.: 44.70 3rd Qu.: 18.38 3rd Qu.:24.975 3rd Qu.:0.090 3rd Qu.:21.000 3rd Qu.:4.265 3rd Qu.: 42.00 3rd Qu.: 333.8 3rd Qu.:25.90 3rd Qu.:2.190 3rd Qu.: 2625 3rd Qu.: 601.8 3rd Qu.:37.20 3rd Qu.: 60.167 3rd Qu.:150.00 3rd Qu.: 0.580 3rd Qu.:14.30 3rd Qu.:36.50 3rd Qu.: 58.00 3rd Qu.: 1.330 3rd Qu.:0.020 3rd Qu.:-1 3rd Qu.:32.2 3rd Qu.: 44.12 3rd Qu.:118.50 3rd Qu.:0.11 3rd Qu.:143.5 3rd Qu.:0.270 3rd Qu.: 45.50 3rd Qu.: 41.00 3rd Qu.:103.97 3rd Qu.: 98.25
Max. :7500.0 Max. :620.00 Max. :48.60 Max. :1.70 Max. :1000.00 Max. :505.70 Max. :558.0 Max. :53.000 Max. :136.00 Max. :6795.000 Max. :145.100 Max. :27.10 Max. :98.9 Max. :88.70 Max. :11.950 Max. :142.00 Max. :250.000 Max. :118.90 Max. :52.30 Max. :1726.60 Max. :168.00 Max. :514.0 Max. :10.780 Max. :88.50 Max. :68.400 Max. :52.420 Max. :7.565 Max. :749.500 Max. :0.490 Max. :2.790 Max. :12.800 Max. :43.010 Max. :33.88 Max. :360.600 Max. :15.00 Max. :50000.0 Max. :113.30 Max. :161.90 Max. :60.000 Max. :2.090 Max. :60.000 Max. :7.300 Max. :1858.00 Max. :1176.0 Max. :36.30 Max. :2.620 Max. :70000 Max. :1867.0 Max. :62.20 Max. :5000.000 Max. :190.80 Max. :39.920 Max. :25.30 Max. :50.60 Max. :732.00 Max. :13.480 Max. :0.120 Max. :-1 Max. :50.8 Max. :144.00 Max. :320.00 Max. :0.27 Max. :179.7 Max. :0.510 Max. :110.00 Max. :1600.00 Max. :224.00 Max. :1497.00
NA’s :5838 NA’s :5176 NA’s :5172 NA’s :5149 NA’s :5839 NA’s :5176 NA’s :5149 NA’s :5148 NA’s :5776 NA’s :5838 NA’s :5200 NA’s :5183 NA’s :5149 NA’s :5175 NA’s :5827 NA’s :5447 NA’s :5827 NA’s :5149 NA’s :5149 NA’s :4979 NA’s :5838 NA’s :5149 NA’s :5540 NA’s :5838 NA’s :5170 NA’s :5149 NA’s :5722 NA’s :4979 NA’s :5149 NA’s :5192 NA’s :5126 NA’s :5331 NA’s :5149 NA’s :5176 NA’s :5244 NA’s :5823 NA’s :5183 NA’s :5540 NA’s :5148 NA’s :5827 NA’s :5476 NA’s :5175 NA’s :5171 NA’s :5172 NA’s :5172 NA’s :5127 NA’s :5631 NA’s :5172 NA’s :5244 NA’s :5834 NA’s :5776 NA’s :5149 NA’s :5244 NA’s :5176 NA’s :5176 NA’s :5447 NA’s :5149 NA’s :5605 NA’s :5149 NA’s :5538 NA’s :5369 NA’s :5828 NA’s :5131 NA’s :5244 NA’s :5723 NA’s :5175 NA’s :5170 NA’s :5170

Stosunek dla najmniejszej liczby wystąpień wartości NaN do całkowitej liczby wierszy przed wypełnieniem 81.5427448%
Stosunek dla największej liczby wystąpień wartości NaN do całkowitej liczby wierszy przed wypełnieniem 95.6272519%

Wartości po wypełnieniu

Do wypełnienia danych z tych komórek wykorzystano funkcję ‘fill’, która najpierw wypełni komórki w dół, gdy napotka wartość inną niż NaN, a następnie wypełni w górę.

after_fill <- before_fill %>% 
              group_by(PATIENT_ID) %>%
              fill(names(.), .direction = 'downup') %>% 
              ungroup()

kable(summary(after_fill[, 2:ncol(after_fill)])) %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "100%")
Hypersensitive.cardiac.troponinI hemoglobin Serum.chloride Prothrombin.time procalcitonin eosinophils… Interleukin.2.receptor Alkaline.phosphatase albumin basophil… Interleukin.10 Total.bilirubin Platelet.count monocytes… antithrombin Interleukin.8 indirect.bilirubin Red.blood.cell.distribution.width neutrophils… total.protein Quantification.of.Treponema.pallidum.antibodies Prothrombin.activity HBsAg mean.corpuscular.volume hematocrit White.blood.cell.count Tumor.necrosis.factor.U.03B1. mean.corpuscular.hemoglobin.concentration fibrinogen Interleukin.1ß Urea lymphocyte.count PH.value Red.blood.cell.count Eosinophil.count Corrected.calcium Serum.potassium glucose neutrophils.count Direct.bilirubin Mean.platelet.volume ferritin RBC.distribution.width.SD Thrombin.time X…lymphocyte HCV.antibody.quantification D.D.dimer Total.cholesterol aspartate.aminotransferase Uric.acid HCO3. calcium Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. Lactate.dehydrogenase platelet.large.cell.ratio Interleukin.6 Fibrin.degradation.products monocytes.count PLT.distribution.width globulin X.U.03B3..glutamyl.transpeptidase International.standard.ratio basophil.count… X2019.nCoV.nucleic.acid.detection mean.corpuscular.hemoglobin Activation.of.partial.thromboplastin.time High.sensitivity.C.reactive.protein HIV.antibody.quantification serum.sodium thrombocytocrit ESR glutamic.pyruvic.transaminase eGFR creatinine
Min. : 1.9 Min. : 6.4 Min. : 71.5 Min. : 11.50 Min. : 0.0200 Min. :0.0000 Min. : 61.0 Min. : 17.00 Min. :13.60 Min. :0.0000 Min. : 5.00 Min. : 2.50 Min. : -1.0 Min. : 0.300 Min. : 20.00 Min. : 5.00 Min. : 0.100 Min. :10.6 Min. : 1.7 Min. :31.80 Min. : 0.0200 Min. : 6.00 Min. : 0.000 Min. : 61.60 Min. :14.50 Min. : 0.13 Min. : 4.00 Min. :286.0 Min. : 0.500 Min. : 5.000 Min. : 0.800 Min. : 0.0000 Min. :5.000 Min. : 0.100 Min. :0.0000 Min. :1.650 Min. : 2.760 Min. : 1.000 Min. : 0.06 Min. : 1.600 Min. : 8.50 Min. : 17.8 Min. : 31.30 Min. : 13.00 Min. : 0.00 Min. :0.0200 Min. : 0.210 Min. :0.100 Min. : 6.00 Min. : 43.0 Min. : 6.30 Min. :1.170 Min. : 5 Min. : 110.0 Min. :11.20 Min. : 1.50 Min. : 4.00 Min. : 0.0100 Min. : 8.0 Min. :10.1 Min. : 3.00 Min. : 0.840 Min. :0.00000 Min. :-1 Min. :20.40 Min. : 21.80 Min. : 0.10 Min. :0.0500 Min. :115.4 Min. :0.0100 Min. : 1.00 Min. : 5.00 Min. : 2.00 Min. : 11.00
1st Qu.: 2.7 1st Qu.:114.0 1st Qu.: 98.8 1st Qu.: 13.50 1st Qu.: 0.0400 1st Qu.:0.0000 1st Qu.: 513.0 1st Qu.: 54.00 1st Qu.:28.40 1st Qu.:0.1000 1st Qu.: 5.00 1st Qu.: 7.20 1st Qu.:121.0 1st Qu.: 3.100 1st Qu.: 77.00 1st Qu.: 9.90 1st Qu.: 3.600 1st Qu.:11.9 1st Qu.:65.1 1st Qu.:62.20 1st Qu.: 0.0400 1st Qu.: 70.00 1st Qu.: 0.000 1st Qu.: 86.80 1st Qu.:33.80 1st Qu.: 4.83 1st Qu.: 7.00 1st Qu.:334.0 1st Qu.: 3.260 1st Qu.: 5.000 1st Qu.: 3.820 1st Qu.: 0.4900 1st Qu.:6.000 1st Qu.: 3.700 1st Qu.:0.0000 1st Qu.:2.270 1st Qu.: 3.920 1st Qu.: 5.630 1st Qu.: 2.97 1st Qu.: 3.200 1st Qu.:10.20 1st Qu.: 422.6 1st Qu.: 38.30 1st Qu.: 15.70 1st Qu.: 4.40 1st Qu.:0.0400 1st Qu.: 0.510 1st Qu.:2.970 1st Qu.: 20.00 1st Qu.: 184.2 1st Qu.:21.00 1st Qu.:2.000 1st Qu.: 72 1st Qu.: 225.0 1st Qu.:26.40 1st Qu.: 7.67 1st Qu.: 4.00 1st Qu.: 0.2800 1st Qu.:11.3 1st Qu.:30.1 1st Qu.: 21.00 1st Qu.: 1.030 1st Qu.:0.01000 1st Qu.:-1 1st Qu.:29.70 1st Qu.: 35.60 1st Qu.: 8.60 1st Qu.:0.0700 1st Qu.:137.2 1st Qu.:0.1400 1st Qu.: 15.00 1st Qu.: 15.00 1st Qu.: 66.70 1st Qu.: 58.00
Median : 12.9 Median :126.0 Median :101.7 Median : 14.30 Median : 0.1000 Median :0.1000 Median : 778.0 Median : 68.00 Median :33.05 Median :0.2000 Median : 7.50 Median : 10.30 Median :180.0 Median : 6.000 Median : 88.00 Median : 17.10 Median : 5.300 Median :12.5 Median :80.9 Median :66.70 Median : 0.0500 Median : 86.00 Median : 0.010 Median : 89.80 Median :36.90 Median : 7.33 Median : 8.70 Median :343.0 Median : 4.410 Median : 5.000 Median : 5.600 Median : 0.7900 Median :6.500 Median : 4.160 Median :0.0100 Median :2.360 Median : 4.330 Median : 6.960 Median : 5.42 Median : 4.600 Median :10.80 Median : 826.8 Median : 40.60 Median : 16.70 Median :12.40 Median :0.0600 Median : 1.350 Median :3.590 Median : 28.50 Median : 243.4 Median :23.20 Median :2.100 Median : 332 Median : 338.0 Median :31.40 Median : 25.36 Median : 7.40 Median : 0.4000 Median :12.6 Median :33.1 Median : 33.00 Median : 1.100 Median :0.01000 Median :-1 Median :30.90 Median : 39.40 Median : 51.90 Median :0.0900 Median :140.1 Median :0.2000 Median : 31.00 Median : 23.00 Median : 89.20 Median : 76.00
Mean : 958.5 Mean :125.1 Mean :102.3 Mean : 15.52 Mean : 0.7299 Mean :0.5679 Mean : 968.3 Mean : 80.78 Mean :32.72 Mean :0.2012 Mean : 18.49 Mean : 15.77 Mean :187.6 Mean : 6.359 Mean : 88.17 Mean : 52.59 Mean : 6.801 Mean :13.0 Mean :77.1 Mean :66.23 Mean : 0.1671 Mean : 82.58 Mean : 6.021 Mean : 90.04 Mean :36.78 Mean : 12.42 Mean : 11.59 Mean :343.4 Mean : 4.486 Mean : 6.364 Mean : 8.374 Mean : 0.9754 Mean :6.410 Mean : 7.774 Mean :0.0342 Mean :2.351 Mean : 4.408 Mean : 8.665 Mean : 7.44 Mean : 9.006 Mean :10.98 Mean : 1486.2 Mean : 42.07 Mean : 17.91 Mean :15.75 Mean :0.1052 Mean : 6.434 Mean :3.651 Mean : 41.96 Mean : 271.6 Mean :23.01 Mean :2.094 Mean : 2332 Mean : 453.6 Mean :32.34 Mean : 93.75 Mean : 53.85 Mean : 0.4899 Mean :13.2 Mean :33.5 Mean : 54.88 Mean : 1.236 Mean :0.01596 Mean :-1 Mean :30.93 Mean : 40.75 Mean : 76.05 Mean :0.0956 Mean :140.6 Mean :0.2065 Mean : 35.12 Mean : 34.56 Mean : 83.71 Mean : 99.22
3rd Qu.: 59.4 3rd Qu.:138.0 3rd Qu.:104.6 3rd Qu.: 15.90 3rd Qu.: 0.3500 3rd Qu.:0.7000 3rd Qu.:1190.0 3rd Qu.: 91.00 3rd Qu.:37.40 3rd Qu.:0.3000 3rd Qu.: 14.00 3rd Qu.: 15.40 3rd Qu.:245.0 3rd Qu.: 8.800 3rd Qu.: 98.00 3rd Qu.: 38.60 3rd Qu.: 7.700 3rd Qu.:13.5 3rd Qu.:91.6 3rd Qu.:70.90 3rd Qu.: 0.0700 3rd Qu.: 96.00 3rd Qu.: 0.010 3rd Qu.: 93.40 3rd Qu.:40.10 3rd Qu.: 12.18 3rd Qu.: 12.10 3rd Qu.:351.0 3rd Qu.: 5.620 3rd Qu.: 5.000 3rd Qu.: 9.700 3rd Qu.: 1.2800 3rd Qu.:7.000 3rd Qu.: 4.610 3rd Qu.:0.0500 3rd Qu.:2.430 3rd Qu.: 4.780 3rd Qu.: 9.870 3rd Qu.:10.46 3rd Qu.: 7.500 3rd Qu.:11.60 3rd Qu.: 1519.9 3rd Qu.: 44.10 3rd Qu.: 18.10 3rd Qu.:24.70 3rd Qu.:0.0900 3rd Qu.:12.050 3rd Qu.:4.220 3rd Qu.: 43.00 3rd Qu.: 329.0 3rd Qu.:25.50 3rd Qu.:2.190 3rd Qu.: 1180 3rd Qu.: 576.0 3rd Qu.:37.80 3rd Qu.: 71.96 3rd Qu.:150.00 3rd Qu.: 0.5800 3rd Qu.:14.7 3rd Qu.:36.6 3rd Qu.: 57.00 3rd Qu.: 1.260 3rd Qu.:0.02000 3rd Qu.:-1 3rd Qu.:32.10 3rd Qu.: 44.10 3rd Qu.:118.30 3rd Qu.:0.1000 3rd Qu.:142.7 3rd Qu.:0.2600 3rd Qu.: 47.00 3rd Qu.: 38.00 3rd Qu.:105.00 3rd Qu.: 97.00
Max. :50000.0 Max. :178.0 Max. :140.4 Max. :120.00 Max. :57.1700 Max. :8.6000 Max. :7500.0 Max. :620.00 Max. :48.60 Max. :1.7000 Max. :1000.00 Max. :505.70 Max. :558.0 Max. :53.000 Max. :136.00 Max. :6795.00 Max. :145.100 Max. :27.1 Max. :98.9 Max. :88.70 Max. :11.9500 Max. :142.00 Max. :250.000 Max. :118.90 Max. :52.30 Max. :1726.60 Max. :168.00 Max. :514.0 Max. :10.780 Max. :88.500 Max. :68.400 Max. :52.4200 Max. :7.565 Max. :749.500 Max. :0.4900 Max. :2.790 Max. :12.800 Max. :43.010 Max. :33.88 Max. :360.600 Max. :15.00 Max. :50000.0 Max. :113.30 Max. :161.90 Max. :60.00 Max. :2.0900 Max. :60.000 Max. :7.300 Max. :1858.00 Max. :1176.0 Max. :36.30 Max. :2.620 Max. :70000 Max. :1867.0 Max. :62.20 Max. :5000.00 Max. :190.80 Max. :39.9200 Max. :25.3 Max. :50.6 Max. :732.00 Max. :13.480 Max. :0.12000 Max. :-1 Max. :50.80 Max. :144.00 Max. :320.00 Max. :0.2700 Max. :179.7 Max. :0.5100 Max. :110.00 Max. :1600.00 Max. :224.00 Max. :1497.00
NA’s :1008 NA’s :20 NA’s :32 NA’s :65 NA’s :460 NA’s :20 NA’s :1857 NA’s :18 NA’s :18 NA’s :20 NA’s :1870 NA’s :18 NA’s :20 NA’s :20 NA’s :2266 NA’s :1857 NA’s :35 NA’s :100 NA’s :20 NA’s :18 NA’s :1127 NA’s :65 NA’s :1117 NA’s :20 NA’s :20 NA’s :16 NA’s :1857 NA’s :20 NA’s :752 NA’s :1857 NA’s :18 NA’s :20 NA’s :1657 NA’s :16 NA’s :20 NA’s :43 NA’s :32 NA’s :67 NA’s :20 NA’s :18 NA’s :110 NA’s :1817 NA’s :100 NA’s :752 NA’s :20 NA’s :1117 NA’s :150 NA’s :18 NA’s :18 NA’s :18 NA’s :18 NA’s :32 NA’s :1247 NA’s :18 NA’s :110 NA’s :1832 NA’s :2266 NA’s :20 NA’s :110 NA’s :18 NA’s :18 NA’s :65 NA’s :20 NA’s :2136 NA’s :20 NA’s :752 NA’s :62 NA’s :1147 NA’s :32 NA’s :110 NA’s :835 NA’s :18 NA’s :18 NA’s :18

Stosunek dla najmniejszej liczby wystąpień wartości NaN do całkowitej liczby wierszy po wypełnieniu 0.2620373%
Stosunek dla największej liczby wystąpień wartości NaN do całkowitej liczby wierszy po wypełnieniu 37.1110383%

Dzięki temu zabiegowi uzyskano znaczny spadek liczby komórek zawierających NaN. ### Wybranie konkretnych próbek Ponieważ kilka wierszy przynależy do jednego pacjenta, to dka każdego pacjenta wybrano mediane wartości z każdej kolumny. Dzięki temu uzyska się po jednym wierszy na pacjenta.

data_fill_summarise <- after_fill %>% 
                     group_by(PATIENT_ID) %>%
                     summarise(across(everything(), 
                                      ~median(.x, na.rm = TRUE), 
                                      .names = "{.col}"))
## `summarise()` ungrouping output (override with `.groups` argument)
kable(summary(data_fill_summarise[,-1]))  %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "100%")
Hypersensitive.cardiac.troponinI hemoglobin Serum.chloride Prothrombin.time procalcitonin eosinophils… Interleukin.2.receptor Alkaline.phosphatase albumin basophil… Interleukin.10 Total.bilirubin Platelet.count monocytes… antithrombin Interleukin.8 indirect.bilirubin Red.blood.cell.distribution.width neutrophils… total.protein Quantification.of.Treponema.pallidum.antibodies Prothrombin.activity HBsAg mean.corpuscular.volume hematocrit White.blood.cell.count Tumor.necrosis.factor.U.03B1. mean.corpuscular.hemoglobin.concentration fibrinogen Interleukin.1ß Urea lymphocyte.count PH.value Red.blood.cell.count Eosinophil.count Corrected.calcium Serum.potassium glucose neutrophils.count Direct.bilirubin Mean.platelet.volume ferritin RBC.distribution.width.SD Thrombin.time X…lymphocyte HCV.antibody.quantification D.D.dimer Total.cholesterol aspartate.aminotransferase Uric.acid HCO3. calcium Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. Lactate.dehydrogenase platelet.large.cell.ratio Interleukin.6 Fibrin.degradation.products monocytes.count PLT.distribution.width globulin X.U.03B3..glutamyl.transpeptidase International.standard.ratio basophil.count… X2019.nCoV.nucleic.acid.detection mean.corpuscular.hemoglobin Activation.of.partial.thromboplastin.time High.sensitivity.C.reactive.protein HIV.antibody.quantification serum.sodium thrombocytocrit ESR glutamic.pyruvic.transaminase eGFR creatinine
Min. : 1.90 Min. : 14.1 Min. : 71.5 Min. : 11.50 Min. : 0.0200 Min. :0.0000 Min. : 70.0 Min. : 17.00 Min. :18.50 Min. :0.000 Min. : 5.00 Min. : 2.500 Min. : -1.0 Min. : 0.600 Min. : 42.00 Min. : 5.000 Min. : 1.100 Min. :10.70 Min. : 1.70 Min. :45.20 Min. : 0.0200 Min. : 6.00 Min. : 0.000 Min. : 61.60 Min. :17.8 Min. : 0.800 Min. : 4.00 Min. :299.0 Min. : 0.600 Min. : 5.000 Min. : 0.800 Min. : 0.000 Min. :5.000 Min. : 1.60 Min. :0.00000 Min. :2.060 Min. :2.860 Min. : 1.000 Min. : 0.320 Min. : 1.600 Min. : 8.50 Min. : 17.8 Min. :31.30 Min. : 13.90 Min. : 0.00 Min. :0.020 Min. : 0.210 Min. :1.340 Min. : 7.00 Min. : 81.0 Min. : 9.80 Min. :1.780 Min. : 5.0 Min. : 119.0 Min. :11.20 Min. : 1.500 Min. : 4.0 Min. : 0.0300 Min. : 8.20 Min. :18.50 Min. : 7.00 Min. : 0.840 Min. :0.00000 Min. :-1 Min. :20.80 Min. : 21.80 Min. : 0.1 Min. :0.0500 Min. :115.4 Min. :0.0100 Min. : 1.0 Min. : 5.00 Min. : 2.30 Min. : 11.00
1st Qu.: 2.60 1st Qu.:115.0 1st Qu.: 98.5 1st Qu.: 13.50 1st Qu.: 0.0400 1st Qu.:0.0000 1st Qu.: 460.0 1st Qu.: 54.00 1st Qu.:29.48 1st Qu.:0.100 1st Qu.: 5.00 1st Qu.: 6.975 1st Qu.:129.0 1st Qu.: 3.275 1st Qu.: 79.25 1st Qu.: 9.375 1st Qu.: 3.500 1st Qu.:11.90 1st Qu.:63.70 1st Qu.:63.20 1st Qu.: 0.0400 1st Qu.: 71.00 1st Qu.: 0.000 1st Qu.: 86.67 1st Qu.:33.9 1st Qu.: 4.640 1st Qu.: 6.90 1st Qu.:336.0 1st Qu.: 3.402 1st Qu.: 5.000 1st Qu.: 3.800 1st Qu.: 0.530 1st Qu.:6.000 1st Qu.: 3.81 1st Qu.:0.00000 1st Qu.:2.260 1st Qu.:3.890 1st Qu.: 5.650 1st Qu.: 2.850 1st Qu.: 3.000 1st Qu.:10.20 1st Qu.: 402.0 1st Qu.:38.30 1st Qu.: 15.60 1st Qu.: 5.00 1st Qu.:0.040 1st Qu.: 0.485 1st Qu.:2.960 1st Qu.: 20.00 1st Qu.:189.0 1st Qu.:20.80 1st Qu.:2.013 1st Qu.: 67.5 1st Qu.: 229.0 1st Qu.:26.00 1st Qu.: 5.972 1st Qu.: 4.0 1st Qu.: 0.2900 1st Qu.:11.12 1st Qu.:30.30 1st Qu.: 20.00 1st Qu.: 1.030 1st Qu.:0.01000 1st Qu.:-1 1st Qu.:29.70 1st Qu.: 35.90 1st Qu.: 10.2 1st Qu.:0.0700 1st Qu.:137.3 1st Qu.:0.1500 1st Qu.: 14.0 1st Qu.: 15.00 1st Qu.: 68.61 1st Qu.: 58.00
Median : 11.00 Median :127.0 Median :101.5 Median : 14.30 Median : 0.1000 Median :0.1000 Median : 693.5 Median : 68.00 Median :33.45 Median :0.200 Median : 6.00 Median : 9.900 Median :184.5 Median : 6.300 Median : 88.00 Median : 16.450 Median : 5.200 Median :12.45 Median :77.90 Median :67.10 Median : 0.0500 Median : 87.00 Median : 0.010 Median : 89.60 Median :37.0 Median : 6.740 Median : 8.60 Median :344.0 Median : 4.580 Median : 5.000 Median : 5.275 Median : 0.820 Median :6.500 Median : 4.18 Median :0.01000 Median :2.350 Median :4.230 Median : 6.920 Median : 4.945 Median : 4.600 Median :10.80 Median : 711.6 Median :40.10 Median : 16.60 Median :13.55 Median :0.060 Median : 1.330 Median :3.505 Median : 29.00 Median :245.0 Median :22.90 Median :2.110 Median : 296.0 Median : 325.5 Median :31.00 Median : 22.125 Median : 5.1 Median : 0.4000 Median :12.57 Median :33.15 Median : 31.00 Median : 1.090 Median :0.01000 Median :-1 Median :30.80 Median : 39.45 Median : 52.0 Median :0.0900 Median :139.8 Median :0.2000 Median : 29.0 Median : 22.00 Median : 90.10 Median : 74.50
Mean : 702.23 Mean :126.5 Mean :101.8 Mean : 15.32 Mean : 0.7204 Mean :0.5447 Mean : 933.7 Mean : 80.15 Mean :33.54 Mean :0.206 Mean : 14.91 Mean : 14.796 Mean :189.3 Mean : 6.594 Mean : 88.77 Mean : 38.018 Mean : 6.639 Mean :12.90 Mean :75.95 Mean :66.93 Mean : 0.1325 Mean : 83.13 Mean : 8.427 Mean : 89.63 Mean :37.0 Mean : 8.921 Mean :11.27 Mean :344.2 Mean : 4.578 Mean : 6.438 Mean : 7.849 Mean : 1.083 Mean :6.440 Mean : 4.86 Mean :0.03046 Mean :2.336 Mean :4.312 Mean : 8.278 Mean : 6.926 Mean : 8.085 Mean :10.89 Mean : 1469.4 Mean :41.60 Mean : 17.69 Mean :16.59 Mean :0.112 Mean : 6.245 Mean :3.602 Mean : 40.02 Mean :274.0 Mean :22.53 Mean :2.104 Mean : 2035.3 Mean : 445.1 Mean :31.64 Mean : 86.993 Mean : 45.8 Mean : 0.5349 Mean :12.96 Mean :33.45 Mean : 51.14 Mean : 1.216 Mean :0.01577 Mean :-1 Mean :30.86 Mean : 40.98 Mean : 74.1 Mean :0.1001 Mean :140.0 Mean :0.2068 Mean : 33.7 Mean : 31.95 Mean : 84.95 Mean : 98.82
3rd Qu.: 50.35 3rd Qu.:140.0 3rd Qu.:104.3 3rd Qu.: 15.72 3rd Qu.: 0.3400 3rd Qu.:0.7000 3rd Qu.:1172.5 3rd Qu.: 88.00 3rd Qu.:38.10 3rd Qu.:0.300 3rd Qu.: 12.60 3rd Qu.: 14.125 3rd Qu.:236.2 3rd Qu.: 9.100 3rd Qu.: 98.00 3rd Qu.: 35.125 3rd Qu.: 7.450 3rd Qu.:13.40 3rd Qu.:90.81 3rd Qu.:71.10 3rd Qu.: 0.0700 3rd Qu.: 96.00 3rd Qu.: 0.010 3rd Qu.: 92.50 3rd Qu.:40.4 3rd Qu.:11.480 3rd Qu.:11.68 3rd Qu.:351.0 3rd Qu.: 5.763 3rd Qu.: 5.000 3rd Qu.: 9.200 3rd Qu.: 1.300 3rd Qu.:7.000 3rd Qu.: 4.61 3rd Qu.:0.04000 3rd Qu.:2.420 3rd Qu.:4.620 3rd Qu.: 9.140 3rd Qu.:10.145 3rd Qu.: 6.800 3rd Qu.:11.50 3rd Qu.: 1439.8 3rd Qu.:43.59 3rd Qu.: 17.90 3rd Qu.:25.35 3rd Qu.:0.090 3rd Qu.:10.908 3rd Qu.:4.150 3rd Qu.: 43.25 3rd Qu.:323.4 3rd Qu.:25.02 3rd Qu.:2.190 3rd Qu.: 1065.0 3rd Qu.: 569.2 3rd Qu.:36.70 3rd Qu.: 62.788 3rd Qu.:102.6 3rd Qu.: 0.5600 3rd Qu.:14.30 3rd Qu.:36.50 3rd Qu.: 51.00 3rd Qu.: 1.242 3rd Qu.:0.02000 3rd Qu.:-1 3rd Qu.:32.02 3rd Qu.: 44.27 3rd Qu.:116.5 3rd Qu.:0.1100 3rd Qu.:142.3 3rd Qu.:0.2500 3rd Qu.: 46.0 3rd Qu.: 35.00 3rd Qu.:105.33 3rd Qu.: 96.00
Max. :50000.00 Max. :178.0 Max. :140.0 Max. :104.80 Max. :38.9200 Max. :5.5500 Max. :7500.0 Max. :620.00 Max. :48.60 Max. :1.700 Max. :1000.00 Max. :505.700 Max. :554.0 Max. :35.200 Max. :130.00 Max. :443.000 Max. :145.100 Max. :24.60 Max. :98.70 Max. :80.30 Max. :11.9500 Max. :142.00 Max. :250.000 Max. :118.90 Max. :52.3 Max. :88.100 Max. :70.40 Max. :488.0 Max. :10.590 Max. :88.500 Max. :59.000 Max. :52.420 Max. :7.565 Max. :96.00 Max. :0.38000 Max. :2.790 Max. :6.860 Max. :29.650 Max. :25.190 Max. :360.600 Max. :14.20 Max. :50000.0 Max. :86.90 Max. :161.90 Max. :60.00 Max. :2.090 Max. :60.000 Max. :6.290 Max. :783.00 Max. :993.0 Max. :33.10 Max. :2.560 Max. :70000.0 Max. :1867.0 Max. :58.60 Max. :5000.000 Max. :190.8 Max. :33.9600 Max. :24.20 Max. :49.00 Max. :732.00 Max. :13.480 Max. :0.09000 Max. :-1 Max. :50.80 Max. :137.20 Max. :320.0 Max. :0.2700 Max. :179.7 Max. :0.5100 Max. :106.0 Max. :744.00 Max. :224.00 Max. :1363.00
NA’s :74 NA’s :5 NA’s :7 NA’s :9 NA’s :48 NA’s :5 NA’s :145 NA’s :5 NA’s :5 NA’s :5 NA’s :146 NA’s :5 NA’s :5 NA’s :5 NA’s :159 NA’s :145 NA’s :6 NA’s :11 NA’s :5 NA’s :5 NA’s :86 NA’s :9 NA’s :86 NA’s :5 NA’s :5 NA’s :4 NA’s :145 NA’s :5 NA’s :63 NA’s :145 NA’s :5 NA’s :5 NA’s :129 NA’s :4 NA’s :5 NA’s :8 NA’s :7 NA’s :10 NA’s :5 NA’s :5 NA’s :15 NA’s :148 NA’s :11 NA’s :63 NA’s :5 NA’s :86 NA’s :19 NA’s :5 NA’s :5 NA’s :5 NA’s :5 NA’s :7 NA’s :94 NA’s :5 NA’s :15 NA’s :143 NA’s :159 NA’s :5 NA’s :15 NA’s :5 NA’s :5 NA’s :9 NA’s :5 NA’s :143 NA’s :5 NA’s :63 NA’s :8 NA’s :87 NA’s :7 NA’s :15 NA’s :73 NA’s :5 NA’s :5 NA’s :5

Wariancja

Ponieważ kolumna ‘Hypersensitive cardiac troponinI’ ma bardzo dużą wartość maksymalną, można sprawdzić wariancje każdej z kolumn.

data_process_var<- data_fill_summarise %>% 
                    ungroup() %>%
                    select(-PATIENT_ID) %>%
                    summarise(across(everything(),  
                                     l.fns= ~var(.x, na.rm = T), ~var(.x, na.rm = T)))
                              
data_process_median <- data_fill_summarise %>% 
                    ungroup() %>%
                    select(-PATIENT_ID) %>%
                    summarise(across(everything(), .fns=~median(.x, na.rm = T)))
                              

data_processed_var_median <- bind_rows(col=names(data_process_median), 
                                       var=unlist(data_process_var[1, ], 
                                                  use.names=FALSE), 
                                       median=unlist(data_process_median[1, ],
                                                     use.names=FALSE))


kable(data_processed_var_median)  %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "500px")
col var median
Hypersensitive.cardiac.troponinI 1.964032e+07 11.000
hemoglobin 3.774513e+02 127.000
Serum.chloride 4.209095e+01 101.450
Prothrombin.time 3.018172e+01 14.300
procalcitonin 9.601393e+00 0.100
eosinophils… 8.152250e-01 0.100
Interleukin.2.receptor 6.204319e+05 693.500
Alkaline.phosphatase 2.278591e+03 68.000
albumin 3.295290e+01 33.450
basophil… 3.990000e-02 0.200
Interleukin.10 4.643130e+03 6.000
Total.bilirubin 1.022797e+03 9.900
Platelet.count 8.375741e+03 184.500
monocytes… 1.592388e+01 6.300
antithrombin 2.474903e+02 88.000
Interleukin.8 4.337771e+03 16.450
indirect.bilirubin 7.958923e+01 5.200
Red.blood.cell.distribution.width 2.526058e+00 12.450
neutrophils… 2.692162e+02 77.900
total.protein 3.572654e+01 67.100
Quantification.of.Treponema.pallidum.antibodies 6.013917e-01 0.050
Prothrombin.activity 3.763158e+02 87.000
HBsAg 1.868855e+03 0.010
mean.corpuscular.volume 3.653049e+01 89.600
hematocrit 2.562566e+01 37.000
White.blood.cell.count 5.492334e+01 6.740
Tumor.necrosis.factor.U.03B1. 8.202053e+01 8.600
mean.corpuscular.hemoglobin.concentration 2.629360e+02 344.000
fibrinogen 2.848917e+00 4.580
Interleukin.1ß 4.652517e+01 5.000
Urea 4.999563e+01 5.275
lymphocyte.count 7.719553e+00 0.820
PH.value 4.687833e-01 6.500
Red.blood.cell.count 5.223115e+01 4.180
Eosinophil.count 2.575100e-03 0.010
Corrected.calcium 1.351020e-02 2.350
Serum.potassium 4.388906e-01 4.230
glucose 1.752148e+01 6.920
neutrophils.count 2.775600e+01 4.945
Direct.bilirubin 5.660994e+02 4.600
Mean.platelet.volume 9.880903e-01 10.800
ferritin 1.463976e+07 711.600
RBC.distribution.width.SD 3.114216e+01 40.100
Thrombin.time 7.772115e+01 16.600
X…lymphocyte 1.631137e+02 13.550
HCV.antibody.quantification 4.720360e-02 0.060
D.D.dimer 7.918990e+01 1.330
Total.cholesterol 7.676391e-01 3.505
aspartate.aminotransferase 3.506764e+03 29.000
Uric.acid 1.705143e+04 245.000
HCO3. 1.270170e+01 22.900
calcium 1.692260e-02 2.110
Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. 3.995339e+07 296.000
Lactate.dehydrogenase 1.010520e+05 325.500
platelet.large.cell.ratio 6.266403e+01 31.000
Interleukin.6 1.373100e+05 22.125
Fibrin.degradation.products 3.813263e+03 5.100
monocytes.count 3.208191e+00 0.400
PLT.distribution.width 6.547088e+00 12.575
globulin 2.451536e+01 33.150
X.U.03B3..glutamyl.transpeptidase 5.301597e+03 31.000
International.standard.ratio 5.084200e-01 1.090
basophil.count… 1.972000e-04 0.010
X2019.nCoV.nucleic.acid.detection 0.000000e+00 -1.000
mean.corpuscular.hemoglobin 7.770515e+00 30.800
Activation.of.partial.thromboplastin.time 7.604773e+01 39.450
High.sensitivity.C.reactive.protein 5.623949e+03 52.000
HIV.antibody.quantification 1.610300e-03 0.090
serum.sodium 3.792593e+01 139.800
thrombocytocrit 7.210400e-03 0.200
ESR 5.949799e+02 29.000
glutamic.pyruvic.transaminase 2.381624e+03 22.000
eGFR 8.810664e+02 90.100
creatinine 1.654261e+04 74.500

Można zauważyć, że kilka kolumn ma bardzo dużą wariancje w stosunku do mediany. W takim przypadku warto usunąć takie kolumn, jako, że mogą przeszkodzić w kolejnych analizach i w tworzeniu klasyfikatora. Zostanie to zrobione w sekcji poświęconej klasyfikatorowi, ponieważ warto najpierw najpierw pokazać je na wykresie. ### Wykresy Za pomocą poniższego wykresu interaktywnego, można wybrać do pokazania przebieg wartości danej kolumny lub wybrać kolumny dla wartości y oraz x, aby zobaczyć zależności.

n <- names(data_fill_summarise %>% select(!PATIENT_ID))
nn <- abbreviate(n)
## Warning in abbreviate(n): 'abbreviate' użyte ze znakami nie będącymi ASCII
buttons <- list()
buttons_x <- list()
id = 1

for (name in n ){
  ly <- list(method = "update", 
            label = paste(nn[[name]], '(', id,  ') as y', sep=''),
            args = list(list(
              y=list(data_fill_summarise[[name]])), 
              list(yaxis = list(title = name))
            ))
  
    lx <- list(method = "update", 
            label = paste(nn[[name]], '(', id,  ') as x', sep=''),
            args = list(list(
              x=list(data_fill_summarise[[name]])), 
              list(xaxis = list(title = name, domain = c(0.1, 1)))
            ))
  
  buttons <- c(buttons, list(ly))
  buttons_x <- c(buttons_x, list(lx))
  id <- id + 1
}
lx <- list(method = "update", 
            label = 'None',
            args = list(list(
              x=list(seq(nrow(data_fill_summarise)))), 
              list(xaxis = list(title = 'row_id', domain = c(0.1, 1)))))
              

buttons_x <- c(list(lx), buttons_x)
fig_many <- plot_ly(data_fill_summarise, 
               x = ~seq(nrow(data_fill_summarise)), 
               y = ~data_fill_summarise[[name[1]]], alpha = 0.3)
fig_many <- fig_many %>% add_markers(marker = list(line = list(color = "black", width = 0.5)))

fig_many <- fig_many %>% layout(
  title = "Plot of one or the relationship between columns.",
  xaxis = list(domain = c(0.1, 1), title = 'row_id'),
  yaxis = list(title = name[1]),
  updatemenus = list(
    list(y = 0.8,
         buttons = buttons
         ),
    list(y = 0.6,
         buttons = buttons_x
         )
    )
  )

fig_many

Korelacja

Za pomocą korelacji można sprawdzić czy nie ma zależności pomiędzy kolumnami. Jeśli istnieją, to pewne kolumny będą zbędne i będzie można wyrzucić ze zbioru.

Uznano, że jeżeli współczynnik korelacji będzie większy bądź równy 0.8, to oznacza, że kolumny są skorelowane.

correl <- cor(data_fill_summarise[-1], use='complete.obs')
## Warning in cor(data_fill_summarise[-1], use = "complete.obs"): odchylenie
## standardowe wynosi zero
correl_table <- as_tibble(correl) %>% mutate(from=names(correl))

kable(correl_table)  %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "500px")
Hypersensitive.cardiac.troponinI hemoglobin Serum.chloride Prothrombin.time procalcitonin eosinophils… Interleukin.2.receptor Alkaline.phosphatase albumin basophil… Interleukin.10 Total.bilirubin Platelet.count monocytes… antithrombin Interleukin.8 indirect.bilirubin Red.blood.cell.distribution.width neutrophils… total.protein Quantification.of.Treponema.pallidum.antibodies Prothrombin.activity HBsAg mean.corpuscular.volume hematocrit White.blood.cell.count Tumor.necrosis.factor.U.03B1. mean.corpuscular.hemoglobin.concentration fibrinogen Interleukin.1ß Urea lymphocyte.count PH.value Red.blood.cell.count Eosinophil.count Corrected.calcium Serum.potassium glucose neutrophils.count Direct.bilirubin Mean.platelet.volume ferritin RBC.distribution.width.SD Thrombin.time X…lymphocyte HCV.antibody.quantification D.D.dimer Total.cholesterol aspartate.aminotransferase Uric.acid HCO3. calcium Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. Lactate.dehydrogenase platelet.large.cell.ratio Interleukin.6 Fibrin.degradation.products monocytes.count PLT.distribution.width globulin X.U.03B3..glutamyl.transpeptidase International.standard.ratio basophil.count… X2019.nCoV.nucleic.acid.detection mean.corpuscular.hemoglobin Activation.of.partial.thromboplastin.time High.sensitivity.C.reactive.protein HIV.antibody.quantification serum.sodium thrombocytocrit ESR glutamic.pyruvic.transaminase eGFR creatinine
1.0000000 0.3090031 -0.1514645 0.3980390 0.1842243 -0.2579785 0.7003151 0.6879387 -0.3550955 -0.1151775 0.0800379 0.7305316 -0.3910918 -0.3775635 -0.3288251 0.2179479 0.4189153 0.4528826 0.3758602 -0.2290173 0.2139383 -0.3401214 0.0476141 0.3900092 0.2630026 0.4800134 0.1850152 0.0710972 -0.1776919 -0.1007560 0.7522036 -0.2673368 -0.3087319 -0.0191184 -0.2505200 0.1400971 -0.0343477 -0.0959208 0.5034699 0.8398009 0.0749452 0.1044471 0.3933478 0.2070382 -0.3530780 -0.0320244 0.3017633 0.1452748 0.3336605 0.5465737 -0.1284160 -0.3552700 0.5325194 0.4411611 0.1356697 0.6089168 0.2909441 0.2816119 0.2995470 0.3047038 0.4708363 0.3926176 0.0965646 NA 0.2992647 -0.1549458 0.6349779 -0.0433099 0.1502153 -0.4558767 -0.0252301 0.2778420 -0.4605798 0.2257688
0.3090031 1.0000000 0.1810569 0.0382213 0.1676988 0.0874823 0.2947947 0.1844285 0.0813186 -0.1028427 0.0792011 0.3478646 -0.2956977 0.0583325 -0.1567856 -0.0459101 0.3829235 -0.2479188 -0.1381375 0.2312710 0.2660614 0.0661188 -0.2921729 -0.0114770 0.9127091 0.3796424 -0.0628034 0.3197929 -0.1968912 -0.1510211 0.1896620 0.2810759 -0.3550320 0.6025731 0.1291319 -0.0897263 0.2778291 -0.0548264 0.1257392 0.3007155 -0.0716891 0.0346474 -0.3058716 0.1285247 0.1665054 0.0680778 0.0580267 -0.2422309 -0.0687146 0.3654918 0.1550968 -0.0053645 0.1392709 0.1600551 -0.0029766 0.0853344 -0.0568803 0.3690220 0.1808126 0.0869484 -0.1367618 0.0426136 0.1883283 NA 0.1800174 0.0364618 -0.0092149 -0.1545346 0.3859266 -0.3815946 -0.3484926 -0.2000107 0.1210353 -0.0063728
-0.1514645 0.1810569 1.0000000 0.1375053 0.3830471 -0.0273677 0.0545780 0.0952495 -0.1077396 0.1523118 0.1879930 -0.0748420 -0.1956483 -0.1280471 -0.0091506 0.3145619 0.0408059 -0.0593163 0.0251840 -0.0322376 0.3902088 -0.0644876 -0.0383565 -0.1784836 0.2239421 0.2838721 0.2051048 -0.0356771 -0.2217434 0.1819540 0.1741694 0.1966700 -0.1011266 0.2211003 -0.1010265 -0.0021907 0.3546066 -0.1587063 0.2322774 -0.1681559 0.4955146 0.3534044 -0.1654599 0.2212147 0.0157065 0.0866925 0.1447740 -0.1069830 0.2082495 -0.0075445 -0.2814987 -0.2048827 0.2536023 0.4657144 0.5044028 -0.1228004 -0.1047375 0.2413263 0.4472444 0.1996859 -0.0255151 0.1503119 0.4609757 NA -0.1532263 -0.1484664 -0.1028728 0.0938636 0.8344035 -0.1270841 0.0369669 -0.0177794 -0.0971718 0.0839090
0.3980390 0.0382213 0.1375053 1.0000000 0.5973899 -0.2547790 0.6076711 0.3303331 -0.5434632 -0.0518024 -0.0287514 0.4529765 -0.4411533 -0.5168092 -0.4653382 0.2725951 0.3301520 0.1552547 0.5168957 -0.6611779 -0.1247091 -0.9530525 0.1264155 0.1900203 -0.0012916 0.4874862 0.2388218 -0.0488167 -0.4800636 0.1609289 0.6594697 -0.4933711 -0.1446578 -0.1481752 -0.1671540 0.5385248 0.3175438 0.3284598 0.6653062 0.4356759 0.2637485 0.4644739 0.0500288 0.3679043 -0.4986410 -0.0470497 0.6364930 -0.0838046 0.5588319 -0.0018173 0.0411577 -0.4237210 0.7344790 0.6053722 0.2495990 0.4492479 0.5847069 0.2712789 0.4191249 0.1843016 0.2601249 0.9992779 0.4238636 NA 0.0576323 -0.1655444 0.5003933 -0.2943415 0.3728913 -0.4562294 -0.2116838 0.4211762 -0.3135288 0.0668809
0.1842243 0.1676988 0.3830471 0.5973899 1.0000000 -0.2212792 0.3321484 0.0806124 -0.3725470 0.1385401 -0.0147294 0.0796920 -0.3664123 -0.3765443 -0.4333035 0.0293449 0.1325098 0.2686435 0.3442540 -0.3416707 -0.0292209 -0.4491279 -0.1173877 0.0183535 0.1435186 0.5718013 -0.0299245 0.0429310 -0.3668003 -0.0742507 0.5848858 -0.2991765 -0.1355157 0.0174611 -0.2159787 0.0252439 0.1938379 0.3579924 0.6416353 0.0127316 0.4042621 0.4181547 0.1671658 0.4001700 -0.3229484 0.0747764 0.4088930 -0.1964753 0.2647309 0.0879980 -0.0061626 -0.4552528 0.6300564 0.6129884 0.3814426 0.4652115 0.3686684 0.1629651 0.4388754 0.1953624 0.1509763 0.6093625 0.8084308 NA 0.0347825 -0.0225270 0.4493481 -0.2992783 0.4644850 -0.3828781 -0.1701500 -0.0383567 -0.2114159 0.2136953
-0.2579785 0.0874823 -0.0273677 -0.2547790 -0.2212792 1.0000000 -0.4816381 -0.0532359 0.4713006 0.6318460 -0.0536297 -0.1060302 0.3135019 0.4828294 0.1657326 -0.3072045 0.1179633 -0.1605387 -0.7319357 0.4970316 -0.1333605 0.1625446 -0.2122609 0.1378107 -0.0876245 -0.2578909 -0.3385928 0.4363618 -0.1903502 0.1648465 -0.4135664 0.7030217 -0.1163047 -0.0403701 0.8793301 0.1949485 0.0948393 -0.3113629 -0.4751558 -0.2297294 -0.1817210 -0.2331957 -0.0344347 -0.2212843 0.7420387 0.3639310 -0.1105000 0.3592424 -0.3636272 0.1954313 0.3216523 0.6707114 -0.4015080 -0.3947446 -0.2044245 -0.4706342 -0.2918482 -0.1757736 -0.2731519 -0.1497582 -0.1498797 -0.2589159 0.0583089 NA 0.3555468 -0.1059630 -0.4926264 0.2673250 0.0191203 0.2898657 -0.2042048 -0.1799848 0.2338191 -0.0538952
0.7003151 0.2947947 0.0545780 0.6076711 0.3321484 -0.4816381 1.0000000 0.6266870 -0.6125923 -0.2070635 0.1601806 0.6601094 -0.3445819 -0.5525153 -0.5171933 0.3815831 0.4229187 0.2977465 0.6030336 -0.4590403 0.3240370 -0.5322996 0.2934054 0.0652550 0.3121013 0.6070066 0.3305758 -0.0694062 0.0654920 -0.0776918 0.7576126 -0.4846694 -0.2834675 0.0936660 -0.3607242 0.3045213 0.1865584 0.3171844 0.6483504 0.7190193 0.1803913 0.4329089 0.1012627 0.4692360 -0.5909248 -0.1423458 0.3885699 -0.0236401 0.5070108 0.2721160 -0.3947974 -0.5788920 0.6767919 0.7041850 0.2118292 0.7052274 0.5266034 0.5268679 0.4078620 0.4685699 0.3445936 0.6052094 0.2691203 NA -0.0099663 -0.1259129 0.7396206 -0.1286339 0.1821875 -0.3724890 0.1222387 0.2678890 -0.4356152 0.1743956
0.6879387 0.1844285 0.0952495 0.3303331 0.0806124 -0.0532359 0.6266870 1.0000000 -0.4455452 0.1578840 0.1414066 0.6097361 -0.3349623 -0.3586896 -0.2943820 0.4309871 0.4805493 0.4149290 0.2362062 -0.2154628 0.5315726 -0.3246787 0.1378474 0.3558477 0.1300490 0.3947607 0.3525166 0.0271688 -0.1531382 0.0666721 0.5226442 -0.1075708 -0.3524802 -0.0503717 -0.0722155 0.3958766 0.1987950 -0.0324993 0.3841223 0.6016592 0.0329782 0.4669722 0.4325527 0.3156283 -0.2042296 -0.0881063 0.4222412 0.4718722 0.4453646 0.3654745 -0.3173311 -0.3294636 0.4685761 0.5775344 0.0599776 0.3885533 0.4033742 0.1557469 0.1524749 0.5443837 0.6544855 0.3200495 0.1954710 NA 0.2371869 -0.3907039 0.5155409 0.2159772 0.2421988 -0.3735150 0.2244327 0.3937510 -0.4729837 0.2599757
-0.3550955 0.0813186 -0.1077396 -0.5434632 -0.3725470 0.4713006 -0.6125923 -0.4455452 1.0000000 0.0829605 -0.2877756 -0.2882934 0.2898404 0.6724237 0.4172418 -0.3736010 -0.0825071 -0.2724626 -0.7949865 0.8015878 -0.3410700 0.5123223 -0.3510070 -0.0026838 0.1462979 -0.5883589 -0.3412338 0.0086808 0.0032505 0.1223837 -0.5756303 0.6327934 -0.0206912 0.0267947 0.3070353 -0.4492692 -0.1802400 -0.5220758 -0.7276176 -0.3658601 -0.1526348 -0.5423189 -0.1073301 -0.4932327 0.7942448 -0.0674455 -0.4870471 -0.0503673 -0.4665881 0.2227805 0.4022458 0.8633454 -0.6878439 -0.7400500 -0.1455400 -0.4588109 -0.5208901 -0.3043445 -0.2291549 -0.6817372 -0.3366015 -0.5467316 -0.4348922 NA 0.0183993 0.3133523 -0.5901055 0.0958651 -0.1156707 0.2798369 -0.3134659 -0.3529552 0.3789646 -0.0207951
-0.1151775 -0.1028427 0.1523118 -0.0518024 0.1385401 0.6318460 -0.2070635 0.1578840 0.0829605 1.0000000 -0.0095624 0.0666399 0.0593519 0.3131026 -0.0402343 -0.1372842 0.2406486 0.2731926 -0.4416733 0.2459617 0.0262860 0.0498325 -0.1466810 0.1250564 -0.1948492 -0.0890583 -0.1711620 0.2759533 -0.2912064 0.0520150 0.0062345 0.3443989 -0.2006560 -0.0735208 0.4259060 0.2650904 0.0797730 -0.1087953 -0.1143103 -0.0662241 0.0556113 0.0996401 0.2813457 0.0598588 0.4201767 0.2187524 -0.0683962 0.3909316 -0.1077815 0.2112073 0.0360748 0.2795003 -0.0205297 0.0079828 0.0056721 -0.1940021 -0.1467801 0.0216271 -0.0969316 0.2167861 0.1388448 -0.0538476 0.5153256 NA 0.2591986 -0.3858612 -0.2451190 0.3350620 0.1282056 0.0533847 -0.0021327 -0.0115033 -0.0164765 0.0621408
0.0800379 0.0792011 0.1879930 -0.0287514 -0.0147294 -0.0536297 0.1601806 0.1414066 -0.2877756 -0.0095624 1.0000000 0.0486831 -0.1630567 -0.0666654 -0.0027963 0.3988315 -0.0381683 -0.0370531 0.0218380 -0.1121129 0.4436620 0.0099239 0.0331547 -0.4289326 0.0582113 0.1951518 0.3681914 0.0011715 0.1611611 0.2775978 0.0192037 0.1257241 -0.2135091 0.2245559 -0.1296829 0.0130632 -0.1158728 0.1499706 0.1646980 0.0765113 0.2327292 0.0735662 -0.2506728 0.1213397 0.0102230 -0.1462499 -0.1030098 0.0573155 0.0863102 -0.1184203 -0.2455995 -0.4020967 -0.0234283 0.1809886 0.2772163 0.2239724 0.0680947 0.0896419 0.2220848 0.3211876 -0.0709309 -0.0245879 0.0736338 NA -0.3079177 0.0772345 0.0760772 -0.0555324 0.0668798 -0.1186420 -0.0410406 0.0692483 -0.1112860 -0.0511809
0.7305316 0.3478646 -0.0748420 0.4529765 0.0796920 -0.1060302 0.6601094 0.6097361 -0.2882934 0.0666399 0.0486831 1.0000000 -0.3114480 -0.1928123 -0.2513338 0.2547137 0.8639484 0.3256451 0.2026632 -0.0912695 0.2424613 -0.4220731 0.1663149 0.1324094 0.3349626 0.4074319 0.1289871 -0.0194965 -0.1641342 0.1508499 0.5872545 -0.1642332 -0.4291879 0.1303889 -0.1180110 0.3897107 0.0329693 -0.0926059 0.4283628 0.9373167 -0.0315523 0.1220141 0.1242312 0.0559811 -0.2019965 -0.0946356 0.1304505 0.0317821 0.2386778 0.3363288 -0.1600498 -0.1446451 0.3827430 0.3487747 0.0355122 0.3734712 0.0917993 0.5566360 0.2471154 0.3568623 0.2538221 0.4403364 0.1659461 NA 0.0770348 -0.2576386 0.3485024 0.1098666 0.2193127 -0.4070775 0.0376302 0.1114903 -0.2159744 -0.0521219
-0.3910918 -0.2956977 -0.1956483 -0.4411533 -0.3664123 0.3135019 -0.3445819 -0.3349623 0.2898404 0.0593519 -0.1630567 -0.3114480 1.0000000 0.0389492 0.2726410 -0.2884755 -0.1872506 -0.2174102 -0.2351691 0.3551400 -0.1300465 0.3296528 0.3204695 -0.2933674 -0.2841255 -0.2274486 -0.2605076 -0.0739318 0.5066729 -0.1143723 -0.5412885 0.3642304 0.1444717 0.0586711 0.3465992 0.0328022 0.0378419 -0.1617256 -0.4283797 -0.3455713 -0.4415720 -0.5270410 -0.2205896 -0.1030682 0.2407797 0.1013428 -0.3735566 0.2075380 -0.5860381 -0.1056313 0.0296906 0.4105682 -0.5605206 -0.5152761 -0.4636460 -0.2223204 -0.4128226 -0.2460695 -0.5337813 -0.0834071 -0.3641106 -0.4514829 -0.1821533 NA -0.1997099 0.1675716 -0.2937644 0.3502449 -0.3497214 0.9577341 0.3447483 -0.4910935 0.2801776 -0.2112968
-0.3775635 0.0583325 -0.1280471 -0.5168092 -0.3765443 0.4828294 -0.5525153 -0.3586896 0.6724237 0.3131026 -0.0666654 -0.1928123 0.0389492 1.0000000 0.1598341 -0.3112433 -0.0133799 -0.2241494 -0.8124883 0.6514809 -0.1935897 0.4732803 -0.1896121 0.0434262 0.0260621 -0.6162041 -0.1998634 0.2178063 0.0427266 0.0167379 -0.4899764 0.5022971 0.1154986 -0.1037955 0.2194846 -0.2001576 -0.2755028 -0.2968019 -0.7163866 -0.2579619 -0.0366773 -0.3201999 -0.0715942 -0.2963703 0.7326184 0.0491496 -0.5941878 -0.0953373 -0.4103231 0.0594236 0.1879401 0.6709072 -0.5935588 -0.6485240 -0.0562270 -0.4257810 -0.5050610 0.0356312 -0.2088553 -0.3417552 -0.1988647 -0.5163053 -0.2887744 NA 0.1601441 0.1104936 -0.5800599 0.1260111 -0.1757411 0.0597689 -0.2098273 -0.1787774 0.2819261 -0.0843475
-0.3288251 -0.1567856 -0.0091506 -0.4653382 -0.4333035 0.1657326 -0.5171933 -0.2943820 0.4172418 -0.0402343 -0.0027963 -0.2513338 0.2726410 0.1598341 1.0000000 -0.1910411 -0.0968698 -0.4672106 -0.2935090 0.3733854 0.0827931 0.3666999 -0.3212668 -0.1414148 -0.1518509 -0.3465318 -0.3041563 -0.1190128 0.1776776 0.0497925 -0.5520476 0.3403386 0.0078226 0.0838571 0.2300811 -0.2110288 -0.1942712 -0.4185976 -0.3767206 -0.3064042 -0.2178867 -0.3195130 -0.3150168 -0.5787747 0.3257298 0.0070820 -0.3378127 0.2084531 -0.4150858 -0.2788321 0.2827438 0.3144671 -0.4883014 -0.3868160 -0.1614265 -0.5544185 -0.4398382 -0.2677984 -0.2097430 -0.3125551 -0.3300379 -0.4790366 -0.2741626 NA -0.1366338 0.0444249 -0.5138709 0.1093798 -0.0239250 0.3390471 0.1777997 -0.3356507 0.3475057 -0.2880467
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0.3900092 -0.0114770 -0.1784836 0.1900203 0.0183535 0.1378107 0.0652550 0.3558477 -0.0026838 0.1250564 -0.4289326 0.1324094 -0.2933674 0.0434262 -0.1414148 -0.0032080 -0.0279419 0.1903288 0.0525291 -0.1226921 -0.2483061 -0.1909186 -0.2031558 1.0000000 -0.1589695 -0.0497312 -0.0397781 0.3019610 -0.3815091 -0.0723383 0.2747184 -0.1582897 -0.0315354 -0.4688105 0.1294020 0.1606493 0.0883187 -0.2208636 0.0809412 0.2382741 0.1736064 0.2229608 0.6157970 -0.0137419 -0.0716961 0.2562957 0.3937564 0.2083639 0.2419268 0.3918809 0.2929515 0.1593078 0.1910259 0.0476063 0.1324115 0.0178214 0.2935304 -0.0096758 0.1237047 -0.1022451 0.5651296 0.1925131 -0.0505621 NA 0.8199013 -0.4685250 0.2294265 -0.1732665 0.1078506 -0.2697048 0.0002488 0.5269593 -0.2916853 0.3591592
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0.7522036 0.1896620 0.1741694 0.6594697 0.5848858 -0.4135664 0.7576126 0.5226442 -0.5756303 0.0062345 0.0192037 0.5872545 -0.5412885 -0.4899764 -0.5520476 0.3032270 0.3446860 0.4873799 0.6084646 -0.5193216 0.0591751 -0.5327571 0.0379915 0.2747184 0.1617597 0.6275542 0.2365978 0.0726018 -0.3164195 -0.0183581 1.0000000 -0.5481559 -0.3096638 -0.0962845 -0.3765073 0.2157655 0.0154320 0.2004957 0.8001254 0.6502469 0.3652139 0.3993858 0.3479853 0.3865486 -0.6019803 -0.0117338 0.4977046 -0.0899425 0.5016640 0.3580457 -0.3274796 -0.5723226 0.8428192 0.7461404 0.3712445 0.6325513 0.5128824 0.4609837 0.4677771 0.3493955 0.5334115 0.6665499 0.4805674 NA 0.2109969 -0.2960997 0.7213911 -0.3034006 0.3382779 -0.5786015 -0.0943950 0.3289082 -0.5718451 0.3083112
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-0.3087319 -0.3550320 -0.1011266 -0.1446578 -0.1355157 -0.1163047 -0.2834675 -0.3524802 -0.0206912 -0.2006560 -0.2135091 -0.4291879 0.1444717 0.1154986 0.0078226 -0.1844999 -0.4284796 -0.1862007 0.0916520 -0.1207329 -0.0960441 0.0824825 0.2903189 -0.0315354 -0.3628281 -0.3403618 0.0427701 -0.1160975 0.2111657 -0.1802453 -0.3096638 -0.1947563 1.0000000 -0.1431770 -0.0421370 -0.0996884 -0.0128635 0.2309243 -0.2431083 -0.3504500 -0.0690165 -0.1801972 -0.0971172 0.0681386 -0.1353150 0.0658866 -0.1103329 -0.0843730 -0.1441134 -0.5466721 0.0035245 -0.0581169 -0.1001514 -0.1655737 -0.0954496 -0.1453015 -0.0816062 -0.1856198 -0.2013727 -0.0993249 -0.2346339 -0.1366889 -0.1432002 NA -0.0828695 0.3018740 -0.1112623 0.1782008 -0.2169466 0.1552143 0.2187536 0.0331291 0.3414679 -0.3144391
-0.0191184 0.6025731 0.2211003 -0.1481752 0.0174611 -0.0403701 0.0936660 -0.0503717 0.0267947 -0.0735208 0.2245559 0.1303889 0.0586711 -0.1037955 0.0838571 0.0305541 0.2296280 -0.3276759 -0.0497649 0.2226552 0.3011864 0.2038148 -0.1453653 -0.4688105 0.7197390 0.2738403 0.0299769 -0.1814475 0.0470294 -0.0051320 -0.0962845 0.2883311 -0.1431770 1.0000000 -0.0094178 -0.0061092 0.4247910 0.0009563 0.0727186 0.0502825 -0.1568370 -0.1167335 -0.5213116 0.0440477 0.0950253 -0.2674318 -0.0606495 -0.2344827 -0.2000574 -0.0146892 0.0151738 -0.0462261 -0.0671038 0.0553753 -0.0843594 -0.0580498 -0.2355274 0.1868627 0.0440707 0.1959890 -0.4051392 -0.1486051 0.1732249 NA -0.4125248 0.0904684 -0.2032230 -0.0429371 0.1824478 -0.0037783 -0.0368573 -0.3100133 0.4154974 -0.3732979
-0.2505200 0.1291319 -0.1010265 -0.1671540 -0.2159787 0.8793301 -0.3607242 -0.0722155 0.3070353 0.4259060 -0.1296829 -0.1180110 0.3465992 0.2194846 0.2300811 -0.3049202 0.0954322 -0.3116205 -0.4678084 0.2965061 -0.1368103 0.0663270 -0.1958940 0.1294020 -0.0703069 -0.0840891 -0.3653766 0.4238557 -0.1795468 0.1085575 -0.3765073 0.5450969 -0.0421370 -0.0094178 1.0000000 0.2502257 0.1759035 -0.0943547 -0.2846563 -0.2289583 -0.3180490 -0.2336220 -0.1678751 -0.1835102 0.4959962 0.3852296 0.0957148 0.4162022 -0.4167589 0.0554386 0.3290820 0.5160777 -0.3035366 -0.2800524 -0.3263066 -0.4677475 -0.0962891 -0.1273056 -0.3484076 -0.1408303 -0.2175050 -0.1700874 0.0858681 NA 0.3413376 -0.1723645 -0.4018072 0.1294766 -0.0126270 0.3050679 -0.1744413 -0.2058999 0.2526991 -0.1236512
0.1400971 -0.0897263 -0.0021907 0.5385248 0.0252439 0.1949485 0.3045213 0.3958766 -0.4492692 0.2650904 0.0130632 0.3897107 0.0328022 -0.2001576 -0.2110288 0.2478162 0.3766221 -0.1471417 0.1654104 -0.3399369 -0.0016023 -0.6356143 0.1609997 0.1606493 -0.1899341 0.2488668 0.2354991 0.0500750 -0.2242048 0.2217156 0.2157655 -0.0956674 -0.0996884 -0.0061092 0.2502257 1.0000000 0.4857479 0.1247275 0.2807903 0.3129763 -0.0400249 0.2174444 -0.1300877 0.2379719 -0.1759160 0.0245966 0.4312685 0.1769668 0.1927633 -0.0757770 -0.0761981 -0.0287151 0.2987558 0.2812007 -0.0607028 0.0925388 0.2975955 0.2623610 -0.0172720 0.4228189 0.2713266 0.5235792 0.2636439 NA 0.1068677 -0.4252339 0.1465693 -0.0285792 0.1280101 0.0309640 0.1269461 0.3765679 -0.2042609 -0.0903664
-0.0343477 0.2778291 0.3546066 0.3175438 0.1938379 0.0948393 0.1865584 0.1987950 -0.1802400 0.0797730 -0.1158728 0.0329693 0.0378419 -0.2755028 -0.1942712 0.0891452 0.0957682 -0.1706600 0.0356509 -0.1164153 0.0845338 -0.3317551 -0.0206741 0.0883187 0.3392892 0.4359226 0.1255773 -0.2062661 -0.3308251 -0.0506113 0.0154320 0.1595787 -0.0128635 0.4247910 0.1759035 0.4857479 1.0000000 0.0262013 0.1622897 -0.0245220 0.1195242 0.2245242 -0.1241246 0.4048331 0.0056744 -0.1509714 0.5388903 0.0856434 0.1430304 0.0975599 0.0319403 0.0263795 0.1768020 0.2669294 0.1137902 -0.0701556 0.1175731 0.0142370 0.1808905 0.2222633 -0.0160895 0.3160382 0.2530440 NA -0.0752923 -0.2606155 -0.0439148 -0.0787116 0.3887465 0.0709506 -0.0875100 0.1691842 0.1290065 -0.1108564
-0.0959208 -0.0548264 -0.1587063 0.3284598 0.3579924 -0.3113629 0.3171844 -0.0324993 -0.5220758 -0.1087953 0.1499706 -0.0926059 -0.1617256 -0.2968019 -0.4185976 0.2052858 -0.0251399 -0.0201533 0.4650862 -0.4794566 0.1210991 -0.3111788 0.2007336 -0.2208636 -0.0874288 0.2785948 0.3350186 0.0656344 0.0935163 -0.0250539 0.2004957 -0.4410488 0.2309243 0.0009563 -0.0943547 0.1247275 0.0262013 1.0000000 0.4039829 -0.1338665 -0.1250390 0.2258826 -0.1308439 0.5392884 -0.4861949 -0.0471231 0.2974479 -0.0469057 0.0176632 -0.3921215 -0.2502321 -0.5375967 0.2963495 0.3468922 -0.1632574 0.3754966 0.5883942 0.0272205 -0.1330274 0.3299650 -0.1497429 0.3393645 0.3471363 NA -0.1346415 -0.0459651 0.3268841 -0.2384653 -0.2539913 -0.2359034 0.0159297 -0.0083953 -0.1549324 0.0461130
0.5034699 0.1257392 0.2322774 0.6653062 0.6416353 -0.4751558 0.6483504 0.3841223 -0.7276176 -0.1143103 0.1646980 0.4283628 -0.4283797 -0.7163866 -0.3767206 0.4638965 0.2466264 0.2603553 0.7880123 -0.6474278 0.1202582 -0.5382990 0.0390161 0.0809412 0.0960324 0.7785524 0.2767831 -0.0091151 -0.2720502 0.1496683 0.8001254 -0.6107087 -0.2431083 0.0727186 -0.2846563 0.2807903 0.1622897 0.4039829 1.0000000 0.4495181 0.2850054 0.3818691 0.0886167 0.3039607 -0.7591858 0.0351550 0.6139488 -0.0618574 0.3626048 -0.0087354 -0.2785718 -0.6972011 0.7058573 0.7617142 0.3113487 0.5165491 0.5893096 0.4142481 0.4299954 0.4553220 0.3129632 0.6753929 0.5982823 NA 0.0311228 -0.3598364 0.6176411 -0.3670350 0.3871837 -0.4701638 0.0382020 0.2274687 -0.3468863 0.0429263
0.8398009 0.3007155 -0.1681559 0.4356759 0.0127316 -0.2297294 0.7190193 0.6016592 -0.3658601 -0.0662241 0.0765113 0.9373167 -0.3455713 -0.2579619 -0.3064042 0.2229799 0.6411761 0.3911630 0.3335478 -0.2210211 0.1792057 -0.3903563 0.1888297 0.2382741 0.2801136 0.4056423 0.1154399 -0.0049249 -0.1060237 0.0041606 0.6502469 -0.3073988 -0.3504500 0.0502825 -0.2289583 0.3129763 -0.0245220 -0.1338665 0.4495181 1.0000000 0.0571954 0.1295855 0.2062129 0.0406139 -0.3374324 -0.0695262 0.1352855 -0.0134511 0.3495726 0.3974122 -0.1439098 -0.2390103 0.4314899 0.3478781 0.1237754 0.4250594 0.1202789 0.5539313 0.3374610 0.3072958 0.3356389 0.4266157 0.0299704 NA 0.1563713 -0.2333627 0.4335010 0.0437933 0.1381970 -0.4111546 0.0327847 0.2706410 -0.2876959 -0.0031158
0.0749452 -0.0716891 0.4955146 0.2637485 0.4042621 -0.1817210 0.1803913 0.0329782 -0.1526348 0.0556113 0.2327292 -0.0315523 -0.4415720 -0.0366773 -0.2178867 0.0763359 -0.1674202 0.1960919 0.1252229 -0.1860701 -0.0847555 -0.2233152 -0.2328947 0.1736064 -0.0442060 0.2063537 -0.0523073 -0.1199267 -0.1478548 0.0346997 0.3652139 -0.2133373 -0.0690165 -0.1568370 -0.3180490 -0.0400249 0.1195242 -0.1250390 0.2850054 0.0571954 1.0000000 0.4169683 0.1977460 -0.0474272 -0.1205050 -0.0654575 0.1320776 -0.2584126 0.4604108 0.1318101 -0.1906046 -0.1930426 0.3601637 0.4079046 0.9873618 0.0548977 0.1260646 0.2348509 0.8814381 -0.0041405 0.2994278 0.2776411 0.2406300 NA 0.0413501 -0.1835295 0.1672540 -0.3160107 0.3638499 -0.2596907 -0.1501779 0.3942464 -0.2074087 0.2240400
0.1044471 0.0346474 0.3534044 0.4644739 0.4181547 -0.2331957 0.4329089 0.4669722 -0.5423189 0.0996401 0.0735662 0.1220141 -0.5270410 -0.3201999 -0.3195130 0.2055034 0.0890478 0.2535280 0.3925554 -0.5117192 0.2750373 -0.3751983 -0.0309244 0.2229608 0.0098730 0.3294871 0.1231979 0.0513219 -0.2049542 -0.0496045 0.3993858 -0.3947869 -0.1801972 -0.1167335 -0.2336220 0.2174444 0.2245242 0.2258826 0.3818691 0.1295855 0.4169683 1.0000000 0.3008134 0.3143775 -0.3884923 0.0209355 0.4824030 0.0395983 0.7686370 -0.0051810 -0.1519092 -0.4709748 0.6435640 0.7210880 0.3672427 0.1617605 0.4981069 0.1831782 0.4225678 0.2700279 0.5287502 0.4707222 0.3545819 NA 0.1524603 -0.3329163 0.3915843 -0.1072968 0.3487999 -0.4340136 0.0735449 0.5052520 -0.3481542 0.2728574
0.3933478 -0.3058716 -0.1654599 0.0500288 0.1671658 -0.0344347 0.1012627 0.4325527 -0.1073301 0.2813457 -0.2506728 0.1242312 -0.2205896 -0.0715942 -0.3150168 0.0020757 -0.0190532 0.8246578 0.0793307 -0.1440696 -0.0706407 -0.0214997 0.0641757 0.6157970 -0.2822397 0.0063242 -0.0335690 -0.0337282 -0.2125934 -0.1240335 0.3479853 -0.2442398 -0.0971172 -0.5213116 -0.1678751 -0.1300877 -0.1241246 -0.1308439 0.0886167 0.2062129 0.1977460 0.3008134 1.0000000 0.1393168 -0.0910201 -0.0324462 0.2369319 0.3492345 0.3445442 0.4375037 -0.0881563 -0.0605150 0.2306352 0.1633765 0.1390114 0.2493348 0.2022430 -0.2414892 0.0647326 0.0069999 0.6671485 0.0529445 0.0301319 NA 0.3937932 -0.3035678 0.3927158 0.1337550 -0.1136109 -0.2099831 0.1030904 0.3492686 -0.3812995 0.4316053
0.2070382 0.1285247 0.2212147 0.3679043 0.4001700 -0.2212843 0.4692360 0.3156283 -0.4932327 0.0598588 0.1213397 0.0559811 -0.1030682 -0.2963703 -0.5787747 0.2956022 0.0487445 0.2018123 0.3158118 -0.3276132 0.3448085 -0.3354372 0.2862006 -0.0137419 0.1326255 0.4489461 0.5608042 0.0603137 -0.0857176 -0.1662495 0.3865486 -0.1415782 0.0681386 0.0440477 -0.1835102 0.2379719 0.4048331 0.5392884 0.3039607 0.0406139 -0.0474272 0.3143775 0.1393168 1.0000000 -0.3250125 -0.0617801 0.4333563 0.1493722 0.2176817 0.1371705 -0.3911011 -0.4753882 0.4554908 0.5065084 -0.0945621 0.5829454 0.3918398 0.0595816 -0.1008895 0.4924946 0.1229946 0.3749421 0.3858192 NA -0.0067728 -0.0714321 0.4523782 -0.0096263 0.1769045 -0.1739496 0.0347554 0.0886386 -0.4126114 0.2920071
-0.3530780 0.1665054 0.0157065 -0.4986410 -0.3229484 0.7420387 -0.5909248 -0.2042296 0.7942448 0.4201767 0.0102230 -0.2019965 0.2407797 0.7326184 0.3257298 -0.3495871 0.0711631 -0.1984171 -0.9900159 0.7755694 -0.0690701 0.4119016 -0.2826244 -0.0716961 0.1531684 -0.4874915 -0.3212710 0.1081047 -0.0793357 0.0856324 -0.6019803 0.8546539 -0.1353150 0.0950253 0.4959962 -0.1759160 0.0056744 -0.4861949 -0.7591858 -0.3374324 -0.1205050 -0.3884923 -0.0910201 -0.3250125 1.0000000 -0.0245921 -0.4580046 0.1420890 -0.4444733 0.2253288 0.3499320 0.7644492 -0.6386567 -0.6184338 -0.1188989 -0.4880503 -0.5523928 -0.3066280 -0.2177279 -0.3790725 -0.2855586 -0.5074866 -0.2125474 NA 0.0316736 0.1904320 -0.6422888 0.2589046 -0.0318145 0.2527181 -0.2860123 -0.3421594 0.3508309 -0.0390594
-0.0320244 0.0680778 0.0866925 -0.0470497 0.0747764 0.3639310 -0.1423458 -0.0881063 -0.0674455 0.2187524 -0.1462499 -0.0946356 0.1013428 0.0491496 0.0070820 -0.0336769 -0.1048014 -0.0826300 -0.0016183 0.0290645 0.0322620 0.0759500 -0.0581922 0.2562957 -0.2326516 0.0027889 -0.1823801 0.8211721 0.0628184 -0.0544381 -0.0117338 0.0165651 0.0658866 -0.2674318 0.3852296 0.0245966 -0.1509714 -0.0471231 0.0351550 -0.0695262 -0.0654575 0.0209355 -0.0324462 -0.0617801 -0.0245921 1.0000000 -0.0195396 0.0022399 -0.0708211 -0.0159664 0.1381384 0.0741953 0.0004650 0.0332675 -0.0942382 -0.0888519 -0.0205449 0.1017313 -0.0544868 0.1579273 -0.0782036 -0.0402407 0.2144059 NA 0.6750336 -0.0758747 -0.0223061 0.2040044 0.2123422 0.0912287 0.1919677 -0.1466046 -0.0434705 0.0459669
0.3017633 0.0580267 0.1447740 0.6364930 0.4088930 -0.1105000 0.3885699 0.4222412 -0.4870471 -0.0683962 -0.1030098 0.1304505 -0.3735566 -0.5941878 -0.3378127 0.3375962 0.0572960 0.1126348 0.5046739 -0.5719020 -0.0904409 -0.5978872 -0.1014671 0.3937564 0.0307099 0.5601885 0.3248794 -0.0130207 -0.5319130 0.2069887 0.4977046 -0.3562744 -0.1103329 -0.0606495 0.0957148 0.4312685 0.5388903 0.2974479 0.6139488 0.1352855 0.1320776 0.4824030 0.2369319 0.4333563 -0.4580046 -0.0195396 1.0000000 0.2272216 0.4895582 0.0588026 -0.0771861 -0.3580658 0.6248488 0.6088375 0.1012433 0.2743911 0.7584343 -0.0312414 0.1508759 0.2186180 0.4567093 0.6425167 0.3020075 NA 0.2119448 -0.3427822 0.5124552 -0.4402265 0.3014163 -0.3683541 -0.1788735 0.4698066 -0.2641353 0.1421191
0.1452748 -0.2422309 -0.1069830 -0.0838046 -0.1964753 0.3592424 -0.0236401 0.4718722 -0.0503673 0.3909316 0.0573155 0.0317821 0.2075380 -0.0953373 0.2084531 0.0424680 0.0945040 0.1813207 -0.1150459 0.0901896 0.2470792 -0.0270687 0.0388726 0.2083639 -0.3084214 0.0590597 0.0456819 0.0017223 -0.0757172 0.0092503 -0.0899425 0.2262591 -0.0843730 -0.2344827 0.4162022 0.1769668 0.0856434 -0.0469057 -0.0618574 -0.0134511 -0.2584126 0.0395983 0.3492345 0.1493722 0.1420890 0.0022399 0.2272216 1.0000000 -0.1399067 0.0657646 -0.1191782 0.0500206 -0.0672379 0.0649558 -0.2594793 -0.0618379 0.1636131 -0.2810627 -0.3424107 0.2512675 0.2641150 -0.0943227 0.0587090 NA 0.1434819 -0.3433527 0.0442496 0.3610106 -0.1011977 0.1883918 0.1778815 0.0394411 -0.0642934 -0.0784239
0.3336605 -0.0687146 0.2082495 0.5588319 0.2647309 -0.3636272 0.5070108 0.4453646 -0.4665881 -0.1077815 0.0863102 0.2386778 -0.5860381 -0.4103231 -0.4150858 0.2949266 0.0013797 0.3977596 0.4562404 -0.5466055 0.0596690 -0.4660248 0.0159557 0.2419268 -0.0108591 0.2159009 0.2872742 -0.0986635 -0.2559915 0.0810734 0.5016640 -0.4888212 -0.1441134 -0.2000574 -0.4167589 0.1927633 0.1430304 0.0176632 0.3626048 0.3495726 0.4604108 0.7686370 0.3445442 0.2176817 -0.4444733 -0.0708211 0.4895582 -0.1399067 1.0000000 0.1727717 -0.1463058 -0.4300802 0.6878799 0.6273329 0.4306075 0.3473053 0.4959179 0.1171506 0.5210565 0.1546916 0.5780723 0.5613766 0.0281198 NA 0.0708333 -0.0350513 0.5211730 -0.1384014 0.2626842 -0.4802491 -0.0723979 0.7274366 -0.4332333 0.3522578
0.5465737 0.3654918 -0.0075445 -0.0018173 0.0879980 0.1954313 0.2721160 0.3654745 0.2227805 0.2112073 -0.1184203 0.3363288 -0.1056313 0.0594236 -0.2788321 -0.1432439 0.2041206 0.4103786 -0.2059236 0.2874081 -0.0085455 0.0942628 -0.2522827 0.3918809 0.3972309 0.2464470 -0.0996743 0.1423610 -0.2612465 -0.2289943 0.3580457 0.3084766 -0.5466721 -0.0146892 0.0554386 -0.0757770 0.0975599 -0.3921215 -0.0087354 0.3974122 0.1318101 -0.0051810 0.4375037 0.1371705 0.2253288 -0.0159664 0.0588026 0.0657646 0.1727717 1.0000000 0.0725983 0.2407805 0.1339186 0.0456957 0.1499787 0.2471552 -0.0909200 0.1125909 0.2190808 -0.0451525 0.3031644 -0.0028235 -0.0071956 NA 0.3490250 -0.1227070 0.1587950 -0.0041594 0.1783958 -0.1263298 -0.3181458 0.1327757 -0.4871924 0.6249405
-0.1284160 0.1550968 -0.2814987 0.0411577 -0.0061626 0.3216523 -0.3947974 -0.3173311 0.4022458 0.0360748 -0.2455995 -0.1600498 0.0296906 0.1879401 0.2827438 -0.4727844 -0.1122097 -0.2954252 -0.3241863 0.1056014 -0.4100273 -0.0208003 -0.3718132 0.2929515 0.0594024 -0.2571017 -0.4870366 0.1873388 -0.4043290 -0.1359580 -0.3274796 0.2652950 0.0035245 0.0151738 0.3290820 -0.0761981 0.0319403 -0.2502321 -0.2785718 -0.1439098 -0.1906046 -0.1519092 -0.0881563 -0.3911011 0.3499320 0.1381384 -0.0771861 -0.1191782 -0.1463058 0.0725983 1.0000000 0.4010382 -0.2367254 -0.4486269 -0.1936272 -0.3514496 -0.1844078 -0.2593477 -0.0771643 -0.5889188 -0.2390401 0.0374709 -0.1117559 NA 0.2994468 0.0912464 -0.3873870 -0.1409263 0.0525889 0.0157609 -0.3767530 0.0211469 0.2758113 -0.0449332
-0.3552700 -0.0053645 -0.2048827 -0.4237210 -0.4552528 0.6707114 -0.5788920 -0.3294636 0.8633454 0.2795003 -0.4020967 -0.1446451 0.4105682 0.6709072 0.3144671 -0.3660578 0.0449012 -0.2628289 -0.7864103 0.7184968 -0.4209381 0.3456279 -0.2732411 0.1593078 -0.0071639 -0.5281817 -0.3804133 0.1218197 -0.0494816 0.1597178 -0.5723226 0.6017271 -0.0581169 -0.0462261 0.5160777 -0.0287151 0.0263795 -0.5375967 -0.6972011 -0.2390103 -0.1930426 -0.4709748 -0.0605150 -0.4753882 0.7644492 0.0741953 -0.3580658 0.0500206 -0.4300802 0.2407805 0.4010382 1.0000000 -0.6749324 -0.7334201 -0.2098607 -0.5332975 -0.4890402 -0.2097869 -0.2811685 -0.5390298 -0.2119448 -0.4322758 -0.3843973 NA 0.1921555 0.0359629 -0.6168892 0.1706188 -0.1533037 0.4026679 -0.2205197 -0.2018372 0.3384805 -0.0728476
0.5325194 0.1392709 0.2536023 0.7344790 0.6300564 -0.4015080 0.6767919 0.4685761 -0.6878439 -0.0205297 -0.0234283 0.3827430 -0.5605206 -0.5935588 -0.4883014 0.1300495 0.2247050 0.3224972 0.6568487 -0.6305675 0.0862356 -0.6338506 -0.0289622 0.1910259 0.0999760 0.5837188 0.1685687 0.0186128 -0.3562606 -0.1458259 0.8428192 -0.5591793 -0.1001514 -0.0671038 -0.3035366 0.2987558 0.1768020 0.2963495 0.7058573 0.4314899 0.3601637 0.6435640 0.2306352 0.4554908 -0.6386567 0.0004650 0.6248488 -0.0672379 0.6878799 0.1339186 -0.2367254 -0.6749324 1.0000000 0.8822205 0.3475288 0.5173709 0.6019578 0.3247849 0.4447514 0.3765403 0.5184121 0.7385187 0.5192691 NA 0.1231073 -0.1601594 0.6983632 -0.2883031 0.3589719 -0.5431335 -0.0955137 0.4251471 -0.4697215 0.2683181
0.4411611 0.1600551 0.4657144 0.6053722 0.6129884 -0.3947446 0.7041850 0.5775344 -0.7400500 0.0079828 0.1809886 0.3487747 -0.5152761 -0.6485240 -0.3868160 0.3744051 0.2511617 0.2912273 0.6514192 -0.5606912 0.4205461 -0.5225317 -0.0150426 0.0476063 0.1235547 0.6912965 0.2902280 0.0269827 -0.1809822 -0.0168519 0.7461404 -0.4818549 -0.1655737 0.0553753 -0.2800524 0.2812007 0.2669294 0.3468922 0.7617142 0.3478781 0.4079046 0.7210880 0.1633765 0.5065084 -0.6184338 0.0332675 0.6088375 0.0649558 0.6273329 0.0456957 -0.4486269 -0.7334201 0.8822205 1.0000000 0.4115302 0.5024762 0.5862371 0.3175988 0.4826414 0.5590682 0.4529395 0.6105860 0.6059804 NA 0.0351019 -0.2726676 0.6586023 -0.1489159 0.4692248 -0.4938980 0.1208411 0.2983288 -0.4549956 0.2193141
0.1356697 -0.0029766 0.5044028 0.2495990 0.3814426 -0.2044245 0.2118292 0.0599776 -0.1455400 0.0056721 0.2772163 0.0355122 -0.4636460 -0.0562270 -0.1614265 0.0856362 -0.1124543 0.1681366 0.1310120 -0.1490489 -0.0237314 -0.2053035 -0.2520481 0.1324115 0.0342844 0.2516651 -0.0553076 -0.1567471 -0.1385873 0.0313521 0.3712445 -0.1813364 -0.0954496 -0.0843594 -0.3263066 -0.0607028 0.1137902 -0.1632574 0.3113487 0.1237754 0.9873618 0.3672427 0.1390114 -0.0945621 -0.1188989 -0.0942382 0.1012433 -0.2594793 0.4306075 0.1499787 -0.1936272 -0.2098607 0.3475288 0.4115302 1.0000000 0.0531825 0.0787255 0.2810665 0.9212356 0.0186034 0.2531851 0.2622343 0.2261886 NA -0.0045749 -0.1616789 0.1492574 -0.3007876 0.3973442 -0.2872064 -0.1556881 0.3595096 -0.1842491 0.1828912
0.6089168 0.0853344 -0.1228004 0.4492479 0.4652115 -0.4706342 0.7052274 0.3885533 -0.4588109 -0.1940021 0.2239724 0.3734712 -0.2223204 -0.4257810 -0.5544185 0.3871774 0.1781163 0.3834756 0.4829773 -0.3071201 0.1610899 -0.3864678 0.2275847 0.0178214 0.0948435 0.3915041 0.4626031 0.0095255 0.1369924 0.0276635 0.6325513 -0.4508752 -0.1453015 -0.0580498 -0.4677475 0.0925388 -0.0701556 0.3754966 0.5165491 0.4250594 0.0548977 0.1617605 0.2493348 0.5829454 -0.4880503 -0.0888519 0.2743911 -0.0618379 0.3473053 0.2471552 -0.3514496 -0.5332975 0.5173709 0.5024762 0.0531825 1.0000000 0.5199791 0.1677212 0.1237797 0.4151186 0.3318362 0.4474561 0.2567187 NA 0.0006667 0.2223949 0.8657241 -0.1589717 -0.0322612 -0.2957721 0.1379181 0.1002012 -0.4508286 0.3021062
0.2909441 -0.0568803 -0.1047375 0.5847069 0.3686684 -0.2918482 0.5266034 0.4033742 -0.5208901 -0.1467801 0.0680947 0.0917993 -0.4128226 -0.5050610 -0.4398382 0.4166113 -0.0016262 0.0921268 0.5669557 -0.5805838 -0.0840316 -0.5528326 -0.0296593 0.2935304 -0.1228993 0.3278679 0.4204615 0.0920492 -0.1998038 0.2414599 0.5128824 -0.5565374 -0.0816062 -0.2355274 -0.0962891 0.2975955 0.1175731 0.5883942 0.5893096 0.1202789 0.1260646 0.4981069 0.2022430 0.3918398 -0.5523928 -0.0205449 0.7584343 0.1636131 0.4959179 -0.0909200 -0.1844078 -0.4890402 0.6019578 0.5862371 0.0787255 0.5199791 1.0000000 0.0180525 0.1007754 0.2748850 0.5072681 0.5896248 0.2348489 NA 0.2043235 -0.1688542 0.7257946 -0.4817751 -0.0354767 -0.4071294 -0.0552895 0.4829634 -0.3578762 0.2339716
0.2816119 0.3690220 0.2413263 0.2712789 0.1629651 -0.1757736 0.5268679 0.1557469 -0.3043445 0.0216271 0.0896419 0.5566360 -0.2460695 0.0356312 -0.2677984 0.1382459 0.4486630 -0.0656917 0.2575160 -0.0880986 0.0928023 -0.1575724 0.1595086 -0.0096758 0.3489414 0.3512996 0.0576254 0.0805062 0.0181695 -0.0138517 0.4609837 -0.1876936 -0.1856198 0.1868627 -0.1273056 0.2623610 0.0142370 0.0272205 0.4142481 0.5539313 0.2348509 0.1831782 -0.2414892 0.0595816 -0.3066280 0.1017313 -0.0312414 -0.2810627 0.1171506 0.1125909 -0.2593477 -0.2097869 0.3247849 0.3175988 0.2810665 0.1677212 0.0180525 1.0000000 0.3847424 0.3557813 0.0569257 0.2769125 0.3200881 NA 0.0363574 -0.2076185 0.1779706 -0.1443119 0.3706249 -0.2472059 0.0859054 0.0696636 -0.0674496 -0.1363763
0.2995470 0.1808126 0.4472444 0.4191249 0.4388754 -0.2731519 0.4078620 0.1524749 -0.2291549 -0.0969316 0.2220848 0.2471154 -0.5337813 -0.2088553 -0.2097430 0.0905792 0.0561350 0.1831879 0.2428026 -0.2276850 0.0432006 -0.3340775 -0.1994929 0.1237047 0.2202618 0.3920549 -0.0906596 -0.1434127 -0.1745886 -0.0341942 0.4677771 -0.2425653 -0.2013727 0.0440707 -0.3484076 -0.0172720 0.1808905 -0.1330274 0.4299954 0.3374610 0.8814381 0.4225678 0.0647326 -0.1008895 -0.2177279 -0.0544868 0.1508759 -0.3424107 0.5210565 0.2190808 -0.0771643 -0.2811685 0.4447514 0.4826414 0.9212356 0.1237797 0.1007754 0.3847424 1.0000000 0.0570358 0.1648624 0.4286379 0.2442132 NA -0.0004668 -0.1263941 0.2018754 -0.2713137 0.4678883 -0.3901615 -0.1787915 0.3425353 -0.1759720 0.1449397
0.3047038 0.0869484 0.1996859 0.1843016 0.1953624 -0.1497582 0.4685699 0.5443837 -0.6817372 0.2167861 0.3211876 0.3568623 -0.0834071 -0.3417552 -0.3125551 0.4100502 0.3275437 0.1744106 0.3655689 -0.1518816 0.5639013 -0.1778663 0.2392858 -0.1022451 0.0364759 0.4635453 0.4508235 0.0624946 0.1650045 -0.0266873 0.3493955 -0.1410853 -0.0993249 0.1959890 -0.1408303 0.4228189 0.2222633 0.3299650 0.4553220 0.3072958 -0.0041405 0.2700279 0.0069999 0.4924946 -0.3790725 0.1579273 0.2186180 0.2512675 0.1546916 -0.0451525 -0.5889188 -0.5390298 0.3765403 0.5590682 0.0186034 0.4151186 0.2748850 0.3557813 0.0570358 1.0000000 0.1986483 0.1790963 0.4647929 NA -0.0267944 -0.2333849 0.4123268 0.1961525 0.1392599 -0.1087048 0.4695141 0.0463247 -0.2315824 -0.0212822
0.4708363 -0.1367618 -0.0255151 0.2601249 0.1509763 -0.1498797 0.3445936 0.6544855 -0.3366015 0.1388448 -0.0709309 0.2538221 -0.3641106 -0.1988647 -0.3300379 0.2150135 0.0670752 0.4523422 0.2750728 -0.3187638 -0.0521085 -0.2279243 -0.0574080 0.5651296 -0.1863237 0.1451303 0.1599666 0.0339178 -0.2390063 0.0637338 0.5334115 -0.3767710 -0.2346339 -0.4051392 -0.2175050 0.2713266 -0.0160895 -0.1497429 0.3129632 0.3356389 0.2994278 0.5287502 0.6671485 0.1229946 -0.2855586 -0.0782036 0.4567093 0.2641150 0.5780723 0.3031644 -0.2390401 -0.2119448 0.5184121 0.4529395 0.2531851 0.3318362 0.5072681 0.0569257 0.1648624 0.1986483 1.0000000 0.2577240 0.0890226 NA 0.3800986 -0.3530457 0.6011375 -0.1369793 0.0511238 -0.3052569 0.0771761 0.6369609 -0.4862412 0.3757766
0.3926176 0.0426136 0.1503119 0.9992779 0.6093625 -0.2589159 0.6052094 0.3200495 -0.5467316 -0.0538476 -0.0245879 0.4403364 -0.4514829 -0.5163053 -0.4790366 0.2774001 0.3146475 0.1590467 0.5252350 -0.6707541 -0.1283056 -0.9463288 0.1258652 0.1925131 0.0024631 0.4943155 0.2436113 -0.0403464 -0.4872883 0.1630721 0.6665499 -0.5003404 -0.1366889 -0.1486051 -0.1700874 0.5235792 0.3160382 0.3393645 0.6753929 0.4266157 0.2776411 0.4707222 0.0529445 0.3749421 -0.5074866 -0.0402407 0.6425167 -0.0943227 0.5613766 -0.0028235 0.0374709 -0.4322758 0.7385187 0.6105860 0.2622343 0.4474561 0.5896248 0.2769125 0.4286379 0.1790963 0.2577240 1.0000000 0.4321693 NA 0.0632446 -0.1704194 0.4994896 -0.3037145 0.3824376 -0.4667609 -0.2222804 0.4265132 -0.3149523 0.0714459
0.0965646 0.1883283 0.4609757 0.4238636 0.8084308 0.0583089 0.2691203 0.1954710 -0.4348922 0.5153256 0.0736338 0.1659461 -0.1821533 -0.2887744 -0.2741626 0.0658406 0.3045819 0.1485570 0.2259505 -0.2188365 0.1974954 -0.3213795 -0.0806868 -0.0505621 0.0845592 0.5461311 -0.0351940 0.1973807 -0.2968178 -0.0319428 0.4805674 -0.1029378 -0.1432002 0.1732249 0.0858681 0.2636439 0.2530440 0.3471363 0.5982823 0.0299704 0.2406300 0.3545819 0.0301319 0.3858192 -0.2125474 0.2144059 0.3020075 0.0587090 0.0281198 -0.0071956 -0.1117559 -0.3843973 0.5192691 0.6059804 0.2261886 0.2567187 0.2348489 0.3200881 0.2442132 0.4647929 0.0890226 0.4321693 1.0000000 NA 0.0889492 -0.3005974 0.2428908 -0.0474467 0.4985053 -0.2269575 0.0594833 -0.1339377 -0.1162564 0.0349016
NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 1 NA NA NA NA NA NA NA NA NA NA
0.2992647 0.1800174 -0.1532263 0.0576323 0.0347825 0.3555468 -0.0099663 0.2371869 0.0183993 0.2591986 -0.3079177 0.0770348 -0.1997099 0.1601441 -0.1366338 -0.0564609 -0.0254117 0.0604424 -0.0620973 -0.0107608 -0.1214939 -0.0453409 -0.2852008 0.8199013 -0.1285389 -0.0349296 -0.1448905 0.7850273 -0.2425506 -0.1075011 0.2109969 -0.0436212 -0.0828695 -0.4125248 0.3413376 0.1068677 -0.0752923 -0.1346415 0.0311228 0.1563713 0.0413501 0.1524603 0.3937932 -0.0067728 0.0316736 0.6750336 0.2119448 0.1434819 0.0708333 0.3490250 0.2994468 0.1921555 0.1231073 0.0351019 -0.0045749 0.0006667 0.2043235 0.0363574 -0.0004668 -0.0267944 0.3800986 0.0632446 0.0889492 NA 1.0000000 -0.3955790 0.1339441 -0.0556135 0.1226937 -0.2205765 -0.0201076 0.2586064 -0.2757657 0.3369285
-0.1549458 0.0364618 -0.1484664 -0.1655444 -0.0225270 -0.1059630 -0.1259129 -0.3907039 0.3133523 -0.3858612 0.0772345 -0.2576386 0.1675716 0.1104936 0.0444249 -0.2267015 -0.2250578 -0.1496611 -0.1843326 0.2635648 -0.1326115 0.1859026 0.1349882 -0.4685250 0.1310063 -0.3161023 -0.0228839 -0.1757300 0.3390412 -0.0574901 -0.2960997 0.1182985 0.3018740 0.0904684 -0.1723645 -0.4252339 -0.2606155 -0.0459651 -0.3598364 -0.2333627 -0.1835295 -0.3329163 -0.3035678 -0.0714321 0.1904320 -0.0758747 -0.3427822 -0.3433527 -0.0350513 -0.1227070 0.0912464 0.0359629 -0.1601594 -0.2726676 -0.1616789 0.2223949 -0.1688542 -0.2076185 -0.1263941 -0.2333849 -0.3530457 -0.1704194 -0.3005974 NA -0.3955790 1.0000000 0.0679364 0.0490921 -0.2178315 0.1736432 -0.1038571 -0.3231911 0.3221512 -0.1036240
0.6349779 -0.0092149 -0.1028728 0.5003933 0.4493481 -0.4926264 0.7396206 0.5155409 -0.5901055 -0.2451190 0.0760772 0.3485024 -0.2937644 -0.5800599 -0.5138709 0.3430234 0.1280014 0.4097318 0.6491214 -0.4759947 0.0714990 -0.4445034 0.2076236 0.2294265 -0.0301929 0.4318080 0.3416510 -0.0132911 0.0916729 0.0114366 0.7213911 -0.6177578 -0.1112623 -0.2032230 -0.4018072 0.1465693 -0.0439148 0.3268841 0.6176411 0.4335010 0.1672540 0.3915843 0.3927158 0.4523782 -0.6422888 -0.0223061 0.5124552 0.0442496 0.5211730 0.1587950 -0.3873870 -0.6168892 0.6983632 0.6586023 0.1492574 0.8657241 0.7257946 0.1779706 0.2018754 0.4123268 0.6011375 0.4994896 0.2428908 NA 0.1339441 0.0679364 1.0000000 -0.2757215 -0.0220596 -0.3047779 0.2162189 0.2802598 -0.4440007 0.2848627
-0.0433099 -0.1545346 0.0938636 -0.2943415 -0.2992783 0.2673250 -0.1286339 0.2159772 0.0958651 0.3350620 -0.0555324 0.1098666 0.3502449 0.1260111 0.1093798 0.0063870 0.1803651 0.2675817 -0.2687250 0.2587999 0.4896005 0.2370960 0.4478112 -0.1732665 -0.1625246 -0.2719080 -0.0165658 0.0491646 0.2455184 -0.0672509 -0.3034006 0.2950796 0.1782008 -0.0429371 0.1294766 -0.0285792 -0.0787116 -0.2384653 -0.3670350 0.0437933 -0.3160107 -0.1072968 0.1337550 -0.0096263 0.2589046 0.2040044 -0.4402265 0.3610106 -0.1384014 -0.0041594 -0.1409263 0.1706188 -0.2883031 -0.1489159 -0.3007876 -0.1589717 -0.4817751 -0.1443119 -0.2713137 0.1961525 -0.1369793 -0.3037145 -0.0474467 NA -0.0556135 0.0490921 -0.2757215 1.0000000 0.0018833 0.2924349 0.4234423 -0.1945230 0.0835863 -0.1238858
0.1502153 0.3859266 0.8344035 0.3728913 0.4644850 0.0191203 0.1821875 0.2421988 -0.1156707 0.1282056 0.0668798 0.2193127 -0.3497214 -0.1757411 -0.0239250 0.2877064 0.2582761 -0.0651121 0.0753131 -0.0851461 0.2993491 -0.2463999 -0.1457239 0.1078506 0.3503402 0.4334738 0.1500682 0.1218255 -0.4950337 0.1752678 0.3382779 0.1618602 -0.2169466 0.1824478 -0.0126270 0.1280101 0.3887465 -0.2539913 0.3871837 0.1381970 0.3638499 0.3487999 -0.1136109 0.1769045 -0.0318145 0.2123422 0.3014163 -0.1011977 0.2626842 0.1783958 0.0525889 -0.1533037 0.3589719 0.4692248 0.3973442 -0.0322612 -0.0354767 0.3706249 0.4678883 0.1392599 0.0511238 0.3824376 0.4985053 NA 0.1226937 -0.2178315 -0.0220596 0.0018833 1.0000000 -0.3357788 -0.1081659 0.0820215 -0.1440513 0.0910923
-0.4558767 -0.3815946 -0.1270841 -0.4562294 -0.3828781 0.2898657 -0.3724890 -0.3735150 0.2798369 0.0533847 -0.1186420 -0.4070775 0.9577341 0.0597689 0.3390471 -0.3276985 -0.3000268 -0.2444651 -0.2477217 0.3327046 -0.1687182 0.3353058 0.2726511 -0.2697048 -0.3494505 -0.2658673 -0.3083563 -0.1423511 0.5237464 -0.1463879 -0.5786015 0.3553501 0.1552143 -0.0037783 0.3050679 0.0309640 0.0709506 -0.2359034 -0.4701638 -0.4111546 -0.2596907 -0.4340136 -0.2099831 -0.1739496 0.2527181 0.0912287 -0.3683541 0.1883918 -0.4802491 -0.1263298 0.0157609 0.4026679 -0.5431335 -0.4938980 -0.2872064 -0.2957721 -0.4071294 -0.2472059 -0.3901615 -0.1087048 -0.3052569 -0.4667609 -0.2269575 NA -0.2205765 0.1736432 -0.3047779 0.2924349 -0.3357788 1.0000000 0.3433165 -0.3841887 0.2759276 -0.1852764
-0.0252301 -0.3484926 0.0369669 -0.2116838 -0.1701500 -0.2042048 0.1222387 0.2244327 -0.3134659 -0.0021327 -0.0410406 0.0376302 0.3447483 -0.2098273 0.1777997 0.3039393 0.0223691 0.0782634 0.2642131 -0.0425600 0.4313171 0.1330878 0.4701264 0.0002488 -0.3604930 -0.1364015 0.1537550 -0.0710535 0.6408035 -0.0121996 -0.0943950 -0.2255494 0.2187536 -0.0368573 -0.1744413 0.1269461 -0.0875100 0.0159297 0.0382020 0.0327847 -0.1501779 0.0735449 0.1030904 0.0347554 -0.2860123 0.1919677 -0.1788735 0.1778815 -0.0723979 -0.3181458 -0.3767530 -0.2205197 -0.0955137 0.1208411 -0.1556881 0.1379181 -0.0552895 0.0859054 -0.1787915 0.4695141 0.0771761 -0.2222804 0.0594833 NA -0.0201076 -0.1038571 0.2162189 0.4234423 -0.1081659 0.3433165 1.0000000 -0.1595715 0.0364812 -0.1577126
0.2778420 -0.2000107 -0.0177794 0.4211762 -0.0383567 -0.1799848 0.2678890 0.3937510 -0.3529552 -0.0115033 0.0692483 0.1114903 -0.4910935 -0.1787774 -0.3356507 0.2730155 -0.1671202 0.1800617 0.3301822 -0.5278164 -0.1515241 -0.3967137 -0.0302492 0.5269593 -0.1984400 -0.0042751 0.3473751 -0.0621849 -0.4046041 0.1481537 0.3289082 -0.3745040 0.0331291 -0.3100133 -0.2058999 0.3765679 0.1691842 -0.0083953 0.2274687 0.2706410 0.3942464 0.5052520 0.3492686 0.0886386 -0.3421594 -0.1466046 0.4698066 0.0394411 0.7274366 0.1327757 0.0211469 -0.2018372 0.4251471 0.2983288 0.3595096 0.1002012 0.4829634 0.0696636 0.3425353 0.0463247 0.6369609 0.4265132 -0.1339377 NA 0.2586064 -0.3231911 0.2802598 -0.1945230 0.0820215 -0.3841887 -0.1595715 1.0000000 -0.4072655 0.2997837
-0.4605798 0.1210353 -0.0971718 -0.3135288 -0.2114159 0.2338191 -0.4356152 -0.4729837 0.3789646 -0.0164765 -0.1112860 -0.2159744 0.2801776 0.2819261 0.3475057 -0.2888526 -0.0487550 -0.3754741 -0.3527568 0.3562557 -0.2283080 0.2735754 0.0206588 -0.2916853 0.1587826 -0.3140646 -0.3475484 -0.1924271 0.1490965 0.0722144 -0.5718451 0.2023409 0.3414679 0.4154974 0.2526991 -0.2042609 0.1290065 -0.1549324 -0.3468863 -0.2876959 -0.2074087 -0.3481542 -0.3812995 -0.4126114 0.3508309 -0.0434705 -0.2641353 -0.0642934 -0.4332333 -0.4871924 0.2758113 0.3384805 -0.4697215 -0.4549956 -0.1842491 -0.4508286 -0.3578762 -0.0674496 -0.1759720 -0.2315824 -0.4862412 -0.3149523 -0.1162564 NA -0.2757657 0.3221512 -0.4440007 0.0835863 -0.1440513 0.2759276 0.0364812 -0.4072655 1.0000000 -0.8235527
0.2257688 -0.0063728 0.0839090 0.0668809 0.2136953 -0.0538952 0.1743956 0.2599757 -0.0207951 0.0621408 -0.0511809 -0.0521219 -0.2112968 -0.0843475 -0.2880467 0.0361304 -0.1005604 0.3111955 0.0512685 -0.0530645 0.0760564 -0.0063052 -0.2138649 0.3591592 -0.0172558 0.0757404 0.1513592 0.2045414 -0.1504464 -0.1430295 0.3083112 0.0456162 -0.3144391 -0.3732979 -0.1236512 -0.0903664 -0.1108564 0.0461130 0.0429263 -0.0031158 0.2240400 0.2728574 0.4316053 0.2920071 -0.0390594 0.0459669 0.1421191 -0.0784239 0.3522578 0.6249405 -0.0449332 -0.0728476 0.2683181 0.2193141 0.1828912 0.3021062 0.2339716 -0.1363763 0.1449397 -0.0212822 0.3757766 0.0714459 0.0349016 NA 0.3369285 -0.1036240 0.2848627 -0.1238858 0.0910923 -0.1852764 -0.1577126 0.2997837 -0.8235527 1.0000000

Powyższa macierz pokazuje zależności pomiędzy konkretnymi kolumnami. Wygodniej jest jednak umieścić w dwóch kolumnach nazwy skorelowanych kolumn, a w trzeciej umieścić wartości współczynnika korelacji. Odfiltrowano również wartości mniejsze niż wskazaną wartość 0.8.

correl_table_filtered <- correl_table %>% mutate(from=names(correl_table)) %>%
                         pivot_longer(!from, names_to = "to", values_to = "count") %>% 
                         filter(count >= corr_value, from != to) %>%
                         rename(corr=count)

kable(correl_table_filtered)  %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "500px")
from to corr
Hypersensitive.cardiac.troponinI Direct.bilirubin 0.8398009
hemoglobin hematocrit 0.9127091
Serum.chloride serum.sodium 0.8344035
Prothrombin.time International.standard.ratio 0.9992779
procalcitonin basophil.count… 0.8084308
eosinophils… Eosinophil.count 0.8793301
albumin total.protein 0.8015878
albumin calcium 0.8633454
Total.bilirubin indirect.bilirubin 0.8639484
Total.bilirubin Direct.bilirubin 0.9373167
Platelet.count thrombocytocrit 0.9577341
Interleukin.8 Tumor.necrosis.factor.U.03B1. 0.8374025
indirect.bilirubin Total.bilirubin 0.8639484
Red.blood.cell.distribution.width RBC.distribution.width.SD 0.8246578
total.protein albumin 0.8015878
mean.corpuscular.volume mean.corpuscular.hemoglobin 0.8199013
hematocrit hemoglobin 0.9127091
Tumor.necrosis.factor.U.03B1. Interleukin.8 0.8374025
mean.corpuscular.hemoglobin.concentration HCV.antibody.quantification 0.8211721
Urea neutrophils.count 0.8001254
Urea Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. 0.8428192
lymphocyte.count X…lymphocyte 0.8546539
Eosinophil.count eosinophils… 0.8793301
neutrophils.count Urea 0.8001254
Direct.bilirubin Hypersensitive.cardiac.troponinI 0.8398009
Direct.bilirubin Total.bilirubin 0.9373167
Mean.platelet.volume platelet.large.cell.ratio 0.9873618
Mean.platelet.volume PLT.distribution.width 0.8814381
RBC.distribution.width.SD Red.blood.cell.distribution.width 0.8246578
X…lymphocyte lymphocyte.count 0.8546539
HCV.antibody.quantification mean.corpuscular.hemoglobin.concentration 0.8211721
calcium albumin 0.8633454
Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. Urea 0.8428192
Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. Lactate.dehydrogenase 0.8822205
Lactate.dehydrogenase Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. 0.8822205
platelet.large.cell.ratio Mean.platelet.volume 0.9873618
platelet.large.cell.ratio PLT.distribution.width 0.9212356
Interleukin.6 High.sensitivity.C.reactive.protein 0.8657241
PLT.distribution.width Mean.platelet.volume 0.8814381
PLT.distribution.width platelet.large.cell.ratio 0.9212356
International.standard.ratio Prothrombin.time 0.9992779
basophil.count… procalcitonin 0.8084308
mean.corpuscular.hemoglobin mean.corpuscular.volume 0.8199013
High.sensitivity.C.reactive.protein Interleukin.6 0.8657241
serum.sodium Serum.chloride 0.8344035
thrombocytocrit Platelet.count 0.9577341

Poniższa tabela wskaże, z iloma kolumnami dana kolumna jest skorelowana.

correl_table_n_corr <- correl_table_filtered %>% 
                       group_by(from) %>% 
                       summarise(n=n()) %>% filter(n >= 1) 
## `summarise()` ungrouping output (override with `.groups` argument)
kable(correl_table_n_corr)  %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "500px")
from n
albumin 2
Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. 2
basophil.count… 1
calcium 1
Direct.bilirubin 2
Eosinophil.count 1
eosinophils… 1
HCV.antibody.quantification 1
hematocrit 1
hemoglobin 1
High.sensitivity.C.reactive.protein 1
Hypersensitive.cardiac.troponinI 1
indirect.bilirubin 1
Interleukin.6 1
Interleukin.8 1
International.standard.ratio 1
Lactate.dehydrogenase 1
lymphocyte.count 1
mean.corpuscular.hemoglobin 1
mean.corpuscular.hemoglobin.concentration 1
mean.corpuscular.volume 1
Mean.platelet.volume 2
neutrophils.count 1
Platelet.count 1
platelet.large.cell.ratio 2
PLT.distribution.width 2
procalcitonin 1
Prothrombin.time 1
RBC.distribution.width.SD 1
Red.blood.cell.distribution.width 1
Serum.chloride 1
serum.sodium 1
thrombocytocrit 1
Total.bilirubin 2
total.protein 1
Tumor.necrosis.factor.U.03B1. 1
Urea 2
X…lymphocyte 1

% % % Cols to remove % Na podstawie ostatnich tabel, wybrano te kolumny które powinny zostać usunięte z tabeli, z powodu wysokiej korelacji.

correl_table_group_filter <- correl_table_filtered %>% 
                             group_by(from) %>% 
                             filter(from %in% correl_table_n_corr$from) %>%
                             ungroup() %>%
                             arrange(corr) %>%
                             distinct(corr, .keep_all = T)
                            

columns_to_remove <- unique(list(correl_table_group_filter$to)[[1]])

kable(tibble(col_to_remove=columns_to_remove))  %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "500px")
col_to_remove
neutrophils.count
total.protein
basophil.count…
mean.corpuscular.hemoglobin
HCV.antibody.quantification
RBC.distribution.width.SD
serum.sodium
Tumor.necrosis.factor.U.03B1.
Direct.bilirubin
Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP.
X…lymphocyte
calcium
indirect.bilirubin
High.sensitivity.C.reactive.protein
Eosinophil.count
PLT.distribution.width
Lactate.dehydrogenase
hematocrit
thrombocytocrit
platelet.large.cell.ratio
International.standard.ratio

Poniższy wykres interaktywny umożliwi pokazanie zależności pomiędzy skorelowanymi kolumnami.

rows <- nrow(correl_table_group_filter)
cor_buttons <- list()

for (row in 1:rows){
  xcol <- correl_table_filtered[row, ]$from
  ycol <- correl_table_filtered[row, ]$to
  
  ly <- list(method = "update", 
            label = paste(row),
            args = list(list(
              x=list(data_fill_summarise[[xcol]]),
              y=list(data_fill_summarise[[ycol]])
                            ), 
              list(yaxis = list(title = ycol), xaxis = list(title = xcol, 
                                                            domain = c(0.1, 1)))
            )
            )

  cor_buttons <- c(cor_buttons, list(ly))
}
xcol1 <- correl_table_filtered[1, ]$from
ycol1 <- correl_table_filtered[1, ]$to
  
fig_cor <- plot_ly(data_fill_summarise, 
               x = ~data_fill_summarise[[xcol1]], 
               y = ~data_fill_summarise[[ycol1]], alpha = 0.3)
fig_cor <- fig_cor %>% add_markers(marker = list(line = list(color = "black", width = 0.5)))

fig_cor <- fig_cor %>% layout(
  title = "Correlation plot",
  xaxis = list(domain = c(0.1, 1), title = xcol1),
  yaxis = list(title = ycol1),
  updatemenus = list(
    list(y = 0.8,
         buttons = cor_buttons
         )
    )
  )

fig_cor

Klasyfikator

Czyszczenie danych

Do analizy zostaną włączone identyfikator pacjenta (tylko do określenia, który wiersz należy do jakiego pacjenta), wiek, płeć, stan pacjenta (outcome, jako klasa dla klasyfikatora). Dodatkowo z danych krwii, zostaną wszystkie oprócz uzyskane z analizy korelacji a także, tych których wariancja jest za duża.

Dodanie kolumn i usunięcie kolumn o dużej korelacji.

join_data <- new_data_df[, c(1, 3, 4, 7)] %>% # select id, age, gender, outcome
             group_by(PATIENT_ID) %>% 
             unique() %>%
             ungroup()

data_join_filled <- data_fill_summarise %>% 
                   select(-all_of(columns_to_remove)) %>%
                   left_join(y=join_data, by='PATIENT_ID')

Usunięcie kolumn o dużej wariancji:

var_per_median <- 100
var_too_big <- data_processed_var_median %>% filter(abs(var) >= abs(var_per_median*median))
    
kable(var_too_big)  %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "50%")
col var median
Hypersensitive.cardiac.troponinI 1.964032e+07 11.000
Interleukin.2.receptor 6.204319e+05 693.500
Interleukin.10 4.643130e+03 6.000
Total.bilirubin 1.022797e+03 9.900
Interleukin.8 4.337771e+03 16.450
HBsAg 1.868855e+03 0.010
Direct.bilirubin 5.660994e+02 4.600
ferritin 1.463976e+07 711.600
aspartate.aminotransferase 3.506764e+03 29.000
Amino.terminal.brain.natriuretic.peptide.precursor.NT.proBNP. 3.995339e+07 296.000
Lactate.dehydrogenase 1.010520e+05 325.500
Interleukin.6 1.373100e+05 22.125
Fibrin.degradation.products 3.813263e+03 5.100
X.U.03B3..glutamyl.transpeptidase 5.301597e+03 31.000
High.sensitivity.C.reactive.protein 5.623949e+03 52.000
glutamic.pyruvic.transaminase 2.381624e+03 22.000
creatinine 1.654261e+04 74.500
data_unselected_high_var <- data_join_filled %>% select(-any_of(var_too_big$col))

Pozostałe wartości puste zostaną wypełnione wartością ‘-1’.

data_replace_na <-data_unselected_high_var

data_replace_na[is.na(data_replace_na)] <- -1

Ustawienie kolumn ‘outcome’ oraz ‘gender’ jako typ kategoryczny

data_clear <- ungroup(data_replace_na)
data_clear$outcome = as.factor(data_clear$outcome)
data_clear$gender = as.factor(data_clear$gender)

kable(head(data_clear)) %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "100%")
PATIENT_ID hemoglobin Serum.chloride Prothrombin.time procalcitonin eosinophils… Alkaline.phosphatase albumin basophil… Platelet.count monocytes… antithrombin Red.blood.cell.distribution.width neutrophils… Quantification.of.Treponema.pallidum.antibodies Prothrombin.activity mean.corpuscular.volume White.blood.cell.count mean.corpuscular.hemoglobin.concentration fibrinogen Interleukin.1ß Urea lymphocyte.count PH.value Red.blood.cell.count Corrected.calcium Serum.potassium glucose Mean.platelet.volume Thrombin.time D.D.dimer Total.cholesterol Uric.acid HCO3. monocytes.count globulin X2019.nCoV.nucleic.acid.detection Activation.of.partial.thromboplastin.time HIV.antibody.quantification ESR eGFR age gender outcome
1 131.0 101.4 13.9 0.09 0.60 54 33.3 0.30 141.0 9.0 -1 11.9 65.8 0.05 91 92.7 9.050 347 3.28 -1.0 7.25 1.555 6.000 4.075 2.385 4.47 7.35 11.50 19.2 1.56 3.90 388.0 26.15 0.62 34.7 -1 37.9 0.09 41 68.75 73 1 0
2 148.0 99.9 14.3 0.09 0.00 43 35.3 0.10 301.0 4.8 -1 12.2 81.5 0.06 87 91.3 8.690 348 5.58 5.0 5.50 1.220 6.000 4.630 2.320 4.78 5.91 10.10 17.0 0.96 4.93 178.0 24.50 0.43 35.2 -1 42.3 -1.00 40 92.60 61 1 0
3 110.5 99.1 13.6 0.06 0.05 47 34.9 0.05 203.5 6.0 84 12.7 70.7 0.07 94 94.5 4.515 330 5.33 5.0 2.90 1.235 -1.000 3.555 2.170 3.34 9.02 11.15 16.7 0.98 3.28 151.0 22.30 0.28 33.4 -1 34.8 0.10 66 77.20 70 2 0
4 84.0 100.8 16.3 0.38 1.50 66 33.9 0.20 94.0 3.8 -1 11.3 82.0 0.04 68 118.9 5.990 372 -1.00 -1.0 7.50 0.750 6.000 1.900 2.340 3.84 5.77 10.50 -1.0 1.26 2.56 250.0 22.80 0.23 31.4 -1 -1.0 0.11 72 82.00 74 1 0
5 134.0 99.7 14.6 0.02 3.30 78 40.2 0.30 380.0 7.0 -1 12.0 58.9 0.05 83 87.8 6.140 338 -1.00 16.4 2.30 1.870 6.000 4.510 2.260 3.26 4.84 9.80 -1.0 0.42 2.49 302.0 25.60 0.43 30.1 -1 -1.0 0.08 15 120.00 29 2 0
6 108.0 95.6 12.4 0.10 0.70 80 39.4 0.70 160.0 13.2 105 12.0 61.9 0.04 117 87.3 4.380 341 4.93 -1.0 9.97 1.030 7.438 3.630 2.210 3.39 5.63 12.40 16.0 0.60 4.05 237.6 23.20 0.58 27.7 -1 45.0 0.08 27 47.30 81 2 0

Utworzenie klasyfikatora

Za pomocą ‘rfe’ można sprawdzić, które atrybuty mają największe znaczenie.

control <- rfeControl(functions=rfFuncs,  method="repeatedcv", number=5, repeats=3)

results <- rfe(data_clear[, 2:42], 
               data_clear$outcome, 
               sizes=c(1:40), 
               rfeControl=control)
print(results)
## 
## Recursive feature selection
## 
## Outer resampling method: Cross-Validated (5 fold, repeated 3 times) 
## 
## Resampling performance over subset size:
## 
##  Variables Accuracy  Kappa AccuracySD KappaSD Selected
##          1   0.7922 0.5788    0.05059 0.10365         
##          2   0.8505 0.6981    0.03581 0.07266         
##          3   0.8735 0.7455    0.03475 0.07010         
##          4   0.8883 0.7753    0.02543 0.05090         
##          5   0.8957 0.7902    0.03125 0.06281         
##          6   0.9031 0.8050    0.03210 0.06476         
##          7   0.9096 0.8179    0.03979 0.08045         
##          8   0.9114 0.8216    0.03612 0.07286         
##          9   0.9160 0.8309    0.03816 0.07704         
##         10   0.9114 0.8215    0.03870 0.07820         
##         11   0.9133 0.8253    0.03928 0.07929         
##         12   0.9197 0.8382    0.04021 0.08123         
##         13   0.9216 0.8421    0.03933 0.07926         
##         14   0.9197 0.8383    0.03578 0.07224         
##         15   0.9197 0.8383    0.03868 0.07826         
##         16   0.9124 0.8235    0.04091 0.08260         
##         17   0.9151 0.8290    0.03929 0.07935         
##         18   0.9188 0.8366    0.03800 0.07672         
##         19   0.9161 0.8309    0.03881 0.07844         
##         20   0.9188 0.8365    0.03611 0.07281         
##         21   0.9188 0.8366    0.03718 0.07488         
##         22   0.9142 0.8271    0.04011 0.08106         
##         23   0.9170 0.8328    0.03797 0.07666         
##         24   0.9188 0.8365    0.03687 0.07428         
##         25   0.9161 0.8309    0.03772 0.07613         
##         26   0.9188 0.8366    0.03789 0.07634         
##         27   0.9197 0.8384    0.03835 0.07731         
##         28   0.9206 0.8402    0.03929 0.07940         
##         29   0.9197 0.8384    0.03654 0.07378         
##         30   0.9216 0.8422    0.03890 0.07840         
##         31   0.9216 0.8422    0.03599 0.07251         
##         32   0.9216 0.8421    0.03331 0.06715         
##         33   0.9206 0.8402    0.03678 0.07431         
##         34   0.9206 0.8402    0.03889 0.07850         
##         35   0.9207 0.8403    0.03312 0.06677         
##         36   0.9188 0.8365    0.03677 0.07413         
##         37   0.9225 0.8441    0.03526 0.07105        *
##         38   0.9215 0.8419    0.03685 0.07454         
##         39   0.9188 0.8365    0.03457 0.06970         
##         40   0.9206 0.8403    0.03399 0.06856         
##         41   0.9198 0.8386    0.03796 0.07642         
## 
## The top 5 variables (out of 37):
##    neutrophils..., procalcitonin, lymphocyte.count, monocytes..., D.D.dimer
predictors(results)
##  [1] "neutrophils..."                           
##  [2] "procalcitonin"                            
##  [3] "lymphocyte.count"                         
##  [4] "monocytes..."                             
##  [5] "D.D.dimer"                                
##  [6] "albumin"                                  
##  [7] "White.blood.cell.count"                   
##  [8] "age"                                      
##  [9] "eosinophils..."                           
## [10] "Prothrombin.time"                         
## [11] "Urea"                                     
## [12] "Prothrombin.activity"                     
## [13] "Platelet.count"                           
## [14] "glucose"                                  
## [15] "eGFR"                                     
## [16] "Total.cholesterol"                        
## [17] "Serum.chloride"                           
## [18] "globulin"                                 
## [19] "monocytes.count"                          
## [20] "basophil..."                              
## [21] "Red.blood.cell.distribution.width"        
## [22] "Mean.platelet.volume"                     
## [23] "HCO3."                                    
## [24] "Thrombin.time"                            
## [25] "mean.corpuscular.volume"                  
## [26] "Alkaline.phosphatase"                     
## [27] "fibrinogen"                               
## [28] "Activation.of.partial.thromboplastin.time"
## [29] "PH.value"                                 
## [30] "Uric.acid"                                
## [31] "Red.blood.cell.count"                     
## [32] "ESR"                                      
## [33] "antithrombin"                             
## [34] "Serum.potassium"                          
## [35] "hemoglobin"                               
## [36] "Corrected.calcium"                        
## [37] "Interleukin.1ß"
plot(results, type=c("g", "o"))

Następnie można wybrać, na przykład 10 najlepszych atrybutów.

data_clear_selected_features <- data_clear %>% 
  select(outcome, predictors(results)[1:10])

W kolejnym etapie można podzielić dane na treningowe oraz testowe.

data_to_fit <- data_clear_selected_features

set.seed(5555)

partition_set <- caret::createDataPartition(data_to_fit$outcome, p = .7, list = FALSE)
training <- data_to_fit[ partition_set,]
## Warning: The `i` argument of ``[`()` can't be a matrix as of tibble 3.0.0.
## Convert to a vector.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.
testing  <- data_to_fit[-partition_set,]
rfGrid <- expand.grid(mtry = 2:10)
gridCtrl <- trainControl(method = "repeatedcv",
                         number = 10,
                         repeats = 5)

Do klasyfikacji, wykorzystano model ‘random forest’ z biblioteki caret:

set.seed(232323)
random_forest <- train(outcome ~ .,
                 data = training,
                 method = "rf",
                 trControl = gridCtrl,
                 tuneGrid = rfGrid,)
random_forest
## Random Forest 
## 
## 254 samples
##  10 predictor
##   2 classes: '0', '1' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times) 
## Summary of sample sizes: 229, 228, 228, 228, 230, 229, ... 
## Resampling results across tuning parameters:
## 
##   mtry  Accuracy   Kappa    
##    2    0.9204641  0.8398740
##    3    0.9220974  0.8433467
##    4    0.9219359  0.8432428
##    5    0.9165205  0.8323898
##    6    0.9157538  0.8308132
##    7    0.9164923  0.8323552
##    8    0.9172615  0.8337711
##    9    0.9172615  0.8337881
##   10    0.9149231  0.8289229
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 3.

Za pomoc ‘gridControl’ dobrano optymalny parametr ‘mtry’.

ggplotly(ggplot(random_forest) + theme_bw())

Następnie, można przetestować działanie tego modelu na danych testowych:

rfClasses <- predict(random_forest, newdata = testing)
cmatrix <- confusionMatrix(data = rfClasses, testing$outcome)

cmatrix
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 53  5
##          1  5 44
##                                           
##                Accuracy : 0.9065          
##                  95% CI : (0.8348, 0.9543)
##     No Information Rate : 0.5421          
##     P-Value [Acc > NIR] : 2.578e-16       
##                                           
##                   Kappa : 0.8118          
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.9138          
##             Specificity : 0.8980          
##          Pos Pred Value : 0.9138          
##          Neg Pred Value : 0.8980          
##              Prevalence : 0.5421          
##          Detection Rate : 0.4953          
##    Detection Prevalence : 0.5421          
##       Balanced Accuracy : 0.9059          
##                                           
##        'Positive' Class : 0               
## 
prob <- as_tibble(predict(random_forest, newdata = testing, type = "prob")) %>% mutate(outcome=testing$outcome) %>% rename(Survived_probability="0", Died_probability="1")

kable(prob %>% arrange(Survived_probability)) %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "400px")
Survived_probability Died_probability outcome
0.000 1.000 1
0.000 1.000 1
0.000 1.000 1
0.000 1.000 1
0.000 1.000 1
0.002 0.998 1
0.002 0.998 1
0.002 0.998 1
0.006 0.994 1
0.006 0.994 1
0.008 0.992 1
0.016 0.984 1
0.018 0.982 1
0.024 0.976 1
0.026 0.974 1
0.028 0.972 1
0.034 0.966 0
0.038 0.962 1
0.044 0.956 1
0.046 0.954 1
0.050 0.950 1
0.050 0.950 1
0.052 0.948 1
0.054 0.946 1
0.062 0.938 1
0.064 0.936 1
0.068 0.932 1
0.076 0.924 1
0.082 0.918 1
0.086 0.914 1
0.094 0.906 1
0.124 0.876 1
0.140 0.860 1
0.148 0.852 1
0.158 0.842 1
0.160 0.840 1
0.174 0.826 1
0.252 0.748 1
0.280 0.720 1
0.282 0.718 1
0.310 0.690 0
0.314 0.686 1
0.324 0.676 0
0.372 0.628 1
0.392 0.608 0
0.402 0.598 1
0.420 0.580 0
0.462 0.538 1
0.464 0.536 1
0.510 0.490 1
0.548 0.452 1
0.548 0.452 1
0.606 0.394 0
0.622 0.378 1
0.630 0.370 0
0.638 0.362 0
0.646 0.354 1
0.650 0.350 0
0.656 0.344 0
0.668 0.332 0
0.688 0.312 0
0.714 0.286 0
0.758 0.242 0
0.776 0.224 0
0.778 0.222 0
0.848 0.152 0
0.864 0.136 0
0.870 0.130 0
0.872 0.128 0
0.876 0.124 0
0.876 0.124 0
0.890 0.110 0
0.894 0.106 0
0.900 0.100 0
0.900 0.100 0
0.912 0.088 0
0.922 0.078 0
0.926 0.074 0
0.948 0.052 0
0.954 0.046 0
0.960 0.040 0
0.968 0.032 0
0.970 0.030 0
0.972 0.028 0
0.980 0.020 0
0.980 0.020 0
0.984 0.016 0
0.988 0.012 0
0.990 0.010 0
0.990 0.010 0
0.990 0.010 0
0.996 0.004 0
0.996 0.004 0
0.996 0.004 0
0.996 0.004 0
0.998 0.002 0
0.998 0.002 0
0.998 0.002 0
0.998 0.002 0
0.998 0.002 0
1.000 0.000 0
1.000 0.000 0
1.000 0.000 0
1.000 0.000 0
1.000 0.000 0
1.000 0.000 0
1.000 0.000 0

Uzyskano trafność około 90%. Natomiast ważniejsze jest trafność czy pacjent przeżyje. Większe skutki niesie ze soba model, który zakwalifikowałby pacjenta, który by umarł (do klasy 1), jako zdolnego do przeżycia (do klasy 0) niż model, który stwierdzi, że pacjent umrze, choć ma duże szanse na przeżycie. W pierwszym przypadku może spowodować, że lekarze nie dbaliby o takiego pacjenta, myśląc, że przeżyje. W tym przypadku miara ‘False positive rate’ wynosi 0.102, a ‘Positive predictive value’ wynosi 91.4%

Ostatecznie, finalny model posiada 500 drzew, a parametr mtry=3:

random_forest$finalModel
## 
## Call:
##  randomForest(x = x, y = y, mtry = param$mtry) 
##                Type of random forest: classification
##                      Number of trees: 500
## No. of variables tried at each split: 3
## 
##         OOB estimate of  error rate: 8.27%
## Confusion matrix:
##     0   1 class.error
## 0 125  12  0.08759124
## 1   9 108  0.07692308

Najważniejsze atrybuty:

row_matrix_names <- rownames(random_forest$finalModel$importance)
values <- random_forest$finalModel$importance
kable(tibble(col=row_matrix_names, MeanDecreaseGini=values) %>% 
      arrange(desc(MeanDecreaseGini))) %>%
  kable_styling(bootstrap_options = "basic", full_width = F) %>%
  scroll_box(width = "100%", height = "400px")
col MeanDecreaseGini
neutrophils… 26.488327
monocytes… 19.261805
lymphocyte.count 15.843889
White.blood.cell.count 14.815900
procalcitonin 14.114685
D.D.dimer 13.211513
albumin 7.540005
age 6.234046
Prothrombin.time 4.507650
eosinophils… 3.513976